Deep active learning and knowledge transfer for rapid discovery of lithium metal battery electrolytes

Domain: biology
Published: 2026-03-27
Editorial outcome: major_revision

Abstract
Designing electrolyte materials for high-energy lithium metal batteries requires navigating vast, discrete chemical spaces, where intricate interphasial and electrolyte chemistries render component interactions largely unclear. Traditional trial-and-error methods struggle with discontinuous electrolyte-performance relationships and inefficient adaptation to new molecular candidates, hindering discovery. Here, we propose a two-stage deep active learning framework with knowledge transfer for rapid electrolyte design. In stage one, deep active learning with deep kernel learning selects informative experiments and models discontinuous relationships between formulation and performance, improving sample efficiency and reducing experimental cost. In stage two, target statistic coding quantifies what was learned and transfers it to new design settings, such as expanded formulation spaces and newly introduced components, using only a small number of additional measurements. Using this framework, we found electrolytes that increase the average lifetime of lithium metal symmetric cells by threefold after three learning iterations, and we rapidly identified improved formulations for Li0||LiNi0.8Co0.1Mn0.1O2 full cells in expanded chemical spaces. This work provides an experiment-driven, sample-efficient route to explore complex electrolyte formulation spaces and quantify inter-component correlations, as well as a realistic, high-cost, small-data benchmark for probabilistic surrogate modeling and sequential decision-making in discrete chemical spaces.

Introduction
Deconvoluting complex systems is central to materials science, chemistry and physics1-4. Key descriptors include the basic components, their properties, and their correlations, which must be decoded for rational design4, 5. However, when multiple independent components are introduced, correlations grow exponentially, making hidden relationships difficult or impossible to identify analytically4-6. To circumvent such complexity, researchers often seek unified theories, such as the structure-property-performance relationships in materials science, which was conventionally derived through extensive trial-and-error experiments6-9. Notably, many materials systems exhibit marked “discontinuity”: changing a single chemical component can induce a sudden rather than incremental change in system behaviour, even when all other variables are kept identical9, 10. In the absence of accurate knowledge of the correlations among those components, building unified theories demands prohibitively costly and time-consuming data acquisition11. In parallel, statistical and machine-learning (ML) approaches have emerged as useful tools to extract hidden relationships from data without requiring full atomic-level understanding2, 4, 12-14. In such methods, purely data-driven models offer flexibility but often lack interpretability8, 15, 16, 17, whereas knowledge-driven approaches leverage empirical rules but can fall short in rigour when applied to large, complex systems6, 15, 18.

Lithium metal batteries (LMBs) using metallic lithium negative electrodes (Li0) are promising next-generation batteries because Li0 possesses the lowest redox potential (-3.04 V vs. standard hydrogen electrode) and high specific capacities (3860 mA h g-1), the combination of which promises the highest possible specific energy9, 19-21. However, the same low redox potential also leads to high reactivity and irreversibility, causing dendrite formation, dead Li0 and capacity loss through continuous Li0-electrolyte reactions3, 22, 23. For decades, stabilizing Li0 has been hampered by the lack of electrolytes that can form chemically, electrochemically, and mechanically stable interfaces24-27. Nevertheless, the pursuit of LMB motivates researchers to generate and verify new electrolyte formulas in the vast design space that includes solvent molecules, additives and salt anions of various structures, as well as their relative ratios 27-30. Buried relationships between these variables and Li0 reversibility are generally attributed to solvation structures, solid-electrolyte interphase (SEI) chemistry and morphology, interfacial ion and mass transport, and charge-transfer processes 31. However, owing to the complexity of Li0-electrolyte interactions, a unified mechanistic description remains elusive 32-35. Unlike the situation in particle reaction kinetics, high-entropy alloys or carbon-nitrogen coupling reactions 12, 14, 36, it has so far been impractical to incorporate generalized physical and chemical principles into predictive electrolyte design for LMBs.

Material discovery for LMBs requires substantial resources and time, as experiments are labour-intensive and often test only a single variable3. Verifying reversibility and stability demands long-term cycling, while promising candidates consume even more time and resources. In contrast, failed or negative results, which would be especially valuable for ML, are frequently neglected, leading to wasted or misdirected efforts 7, 8, 37, 38. The challenge is compounded by large experimental variability, particularly in electrolyte design, where results are often incomparable across studies due to different cell configurations and testing conditions 38-40. To complicate it further, unlike the optimization of nonchemical (particularly numerical) subjects of interest—the examples of which include battery fast-charging protocols16, 18, 41 or tuning electrolyte physical properties42 like solubility, conductivity, and viscosity, which vary continuously—electrolyte design faces a highly discrete search space. This arises because the relationship between components and performance is sensitive to small changes, owing to complex equilibrium and non-equilibrium processes within the cell, especially at the interfaces. As a result, even a single component change can qualitatively alter the underlying chemical interactions, leading to a combinatorial explosion of the design space43. Such discontinuities remain beyond precise chemical intuition and must otherwise be identified through painstaking trial-and-error exploration6, 44.

Pioneering ML-assisted approaches, often coupled with computational screening or robotic experimentation, have shown promise in electrolyte design11, 32, 42, 45. However, these efforts have largely focused on numerically continuous parameter spaces42, 45. Learning methods capable of handling large parameter-performance discontinuities, critical for industrially relevant spaces, remain underdeveloped. Some studies have relied on theory-driven descriptors such as the lowest-unoccupied-molecular-orbital or highest-occupied-molecular-orbital (LUMO/HOMO) theory, ionic conductivity, or atomic ratios, etc. 32, 45; but these are retrospective and capture only known principles rather than uncovering new rules32. Furthermore, exploration was typically restricted to a predefined small parameter space, restricting knowledge transfer to broader chemical domains8, 14. Given the importance of deriving new knowledge directly from experimental data, it is essential to develop advanced ML methods that can effectively explore discontinuous chemical spaces while revealing novel correlation patterns.

To address these challenges, we developed a two-stage optimization framework that leverages deep active learning (DAL) and knowledge transfer for rapid electrolyte optimization (Fig. 1). The first stage employs DAL, which integrates deep kernel learning (DKL) with Thompson sampling to effectively model highly discontinuous component-performance correlations. This approach, based on DKL’s capability for global representation of the electrolyte parameter space, enables efficient exploration of vast chemical spaces with minimal experimental cost and without reliance on empirical knowledge. Subsequently, a target statistic coding (TSC) scheme is used to quantify correlations among components based on both positive and negative outcomes accumulated during the DAL process. This quantified information, comprising substantial new knowledge, serves as the foundation for the second stage of our framework. The second stage involves transferring this accumulated knowledge into DAL optimization processes targeting substantially larger parameter spaces, thereby facilitating identification of high-performance electrolytes beyond the original parameter space. To validate this stepwise DAL workflow, we demonstrate successful knowledge transfer from the optimization of Li0||Li0 symmetric cells to optimization of strictly parameterized high-energy Li metal full cells, as well as to expanded parameter spaces incorporating newly reported molecules from recent literature. From the perspective of battery research, this framework organizes costly cycling experiments into a structured, sample-efficient exploration of electrolyte formulations; from the perspective of machine learning, it provides a realistic, high-cost and small-data testbed for probabilistic surrogate modelling and sequential decision-making in discrete chemical spaces.

Results
In this work, the key components (lithium salts, solvents, additives and their concentrations) were selected to form a parameter space for electrolyte design (detailed in Supplementary Note 1), which includes four Li salts (lithium hexafluorophosphate (LiPF6), lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), lithium bis(fluorosulfonyl)imide (LiFSI), and lithium difluoro(oxalato)borate (LiDFOB)), six solvent molecules (ethylene carbonate (EC), dimethyl carbonate (DMC), 1,2-dimethoxyethane (DME), 1,3-dioxolane (DOL), ethylene sulfite (ES), and propylene carbonate (PC)) and three additive molecules (vinylene carbonate (VC) and fluoroethylene carbonate (FEC), and lithium nitrate (LiNO3), while Li salt concentration is added as an independent component (that is, 1, 2, 5 m in molality). Together, the above components generate a parameter space with 720 electrolyte formulas by applying constraints of each electrolyte having a single Li salt, two solvent molecules with a 1:1 volume ratio, and a single additive molecule (0 or 5 wt.%) (each shown as a square in the gray matrix in Fig. 2a). The detailed electrolyte formulas are indexed in Supplementary Data 1, and for clarity, the denotations of the chemical components are not described in detail here.

Our objective is to determine the optimal electrolyte formulas with long cycle life in a sample-efficient manner (i.e., as few experiments as possible). The major challenges in such an electrolyte optimization problem are (i) the large space of possible electrolyte formulas, while the experimental budget is often limited; (ii) the chemical space for electrolyte optimization is discrete, and its component-performance relationship is largely discontinuous, where an abrupt change in the performance often occurs with the change of a single chemical or element, as illustrated in Fig. 2b; and (iii) the experimental output of the electrolytes is noisy due to the large experimental or measurement variability associated with Li0.

The performance of these electrolytes was evaluated by the cycle life of a Li0||Li0 symmetric cell containing such electrolytes, which was conducted using a protocol of an areal capacity of 2 mA h cm-2 and a current of 0.5 mA cm-2 (Supplementary Fig. 1). The cell lifespan is defined as the number of cycles when the cell ends with a hard short circuit, a soft circuit, or an overpotential greater than 0.5V (Supplementary Fig. 1). A statistical analysis is conducted on the variations among the electrolyte’s components and lifespan within the parameter space, which underscores that even minor adjustments to a single component can induce significant change in cell lifespan (Supplementary Fig. 2), thus confirming the discontinuity nature of the cell performance as a function of electrolyte component resulting from the complex interplay among these components (Fig. 2c).

Active learning (AL) is widely used in many fields46-48, for example, to optimize the fast-charging protocols of lithium-ion batteries (LIBs) under the constraints of battery voltage and temperature49, 508. The objective function of the fast-charging optimization problem is usually smooth; that is, for two similar charging current configurations, their corresponding outputs of the cycle life are close. However, for the black-box functions with rapid oscillations, which are characteristic of the objective function in the electrolyte optimization problem, the representation ability of the commonly-used surrogate model of the Gaussian process is limited because the covariance function used by the Gaussian process is a stationary covariance function, namely, κ(x, x′) = κ((x−x′), 0), where κ and x, x′ stand for the covariance function and the input variables, respectively. For rapidly oscillating objective functions, simply measuring the similarity of the output by the distance between the input variables makes the surrogate model of AL highly inaccurate. In addition, the selection of the covariance function depends on prior knowledge of the optimization objective, which is usually not available.

To address these issues, we propose a DKL-based Gaussian process approach to model the complex structure-property relationships of the chemical space for LMB electrolytes (Fig. 2d). DKL combines the representational power of deep neural networks with the reliable uncertainty estimates of Gaussian processes, which provides a method to automatically determine covariance functions. On one hand, the deep neural network can learn structure-property relationships directly from data, automatically forming adaptive kernel representations and thereby avoiding the need for manually defined covariance kernels with predefined smoothness assumptions, which enhances the representation ability of models. On the other, the nonparametric model automatically calibrates its complexity through the marginal likelihood function of Gaussian processes, making the model resistant to overfitting.

Given a dataset with the variables x and y that represent the electrolyte formulas and cell cycle life, respectively, the inputs can be converted by the DKL as51:

k (x(i),x(j)|ω,θ) = kbase (g(x(i)|ω),g(x(j)|ω)|θ) (1)

where kbase (x(i),x(j)) denotes the base kernel function, θ is the hyperparameter of the base kernel, and g is the nonlinear mapping learned by the deep neural network, which is parameterized by the weights ω. The representational capability of deep neural network-based kernels in DKL largely surpasses that of conventional kernels, such as radial basis functions (RBF) employed in standard Gaussian processes. This enhanced capability is particularly valuable when modeling the objective functions of electrolyte optimization problems, where the deep kernel excels at capturing complex and discontinuous relationships inherent in the chemical parameter space (see Methods for more details), facilitating a substantially more efficient optimization for this challenging problem.

By maximizing the marginal likelihood of DKL, we learn all deep kernel hyperparameters, including the parameter ω of the deep neural network and the parameter θ of the base kernel. The covariance function in (1) can be adaptively learned from the data by utilization of the flexible representational capability of deep neural networks with the reliable uncertainty quantification provided by Gaussian processes. To fully leverage the experimental throughput of parallel evaluations, an acquisition function of Thompson Sampling (see Methods) is then constructed based on the posterior distribution from the surrogate model of DKL. This strategy enables scalable batch-parallel optimization and efficiently sample the parameter space of electrolyte formulas by balancing exploration (i.e., testing regions with high uncertainty) and exploitation (i.e., testing promising regions based on completed experiment results)52.

As illustrated in Supplementary Fig. 2, the space of electrolyte formulas is discrete in the dimensions of Li salts, solvents and additives, but somewhat relatively continuous in salt concentrations (Supplementary Figs. 2d-f), which points to an objective function featuring both discontinuous transitions and continuous variations. This sharp and non-monotonic response of cycle life to single-component changes demonstrates the “rapid oscillations” in the objective function that characterize the electrolyte optimization problem. Therefore, a numerical function of f = (1-|x|)sin(20(1-|x|)6) was set up to simulate the process to verify the efficacy of the DAL approach based on the surrogate model of DKL (Fig. 2e and detailed in Methods). Notably, the DAL approach can adaptively balance the exploration and exploitation processes over the iterations on both high and low oscillation regions (Fig. 2e). Compared with the standard Gaussian process-based active learning (GP-AL), our DAL approach can build a more accurate surrogate model for such a rapidly oscillating objective function (Fig. 2e and Supplementary Fig. 3), as further validated by experimental results (Supplementary Fig. 3e). Even when the training samples are deliberately assigned with large noise, generally arising from minor differences and large errors in lithium metal negative electrode in experiments, the DAL approach efficiently identifies the optimal solution as early as the second iteration (Supplementary Fig. 4). Concurrently, as the iterations progress, DAL continues to refine potential candidate formula points. After three iterations, the mean square error produced by the DAL approach is 42.2% lower than that by GP-AL, and the optimal solution obtained by DAL outperforms GP-AL by 9.9% (discussed in detail in Supplementary Figs. 3 and 4).

As we observed experimentally, electrolytes with longer cell lifespans exhibit a rather scattered distribution due to experimental variability, whereas electrolytes with shorter lifespans occur with a more concentrated distribution (Supplementary Fig. 4). We also assessed different noise levels during numerical simulations, and observed that the DAL approach possesses good and robust performance for diverse noise levels achieving optimal values of x = 0.94 at 5%, 10%, and 20% noise levels (Supplementary Fig. 4). This robustness to noise interference is higher than that of the GP-AL method. The DAL approach showed a marginal 0.4% reduction in performance compared to an 11% decrease in the GP-AL method under a 10% noise level (detailed in Supplementary Note 2).

To demonstrate the overall success of our DAL approach, we ran three DAL iterations with a total number of 128 cells tested, including the first round of random selection (see detailed electrolyte formulas in Supplementary Tables 1-4). Figure 3a clearly shows that as DAL iterates, the mean lifespan of the tested cells experiences a notable increase. Specifically, the mean cycle lives are 41.9, 60.7, 87.7 and 125.1 cycles for the random round and subsequent three iterations, respectively. In addition, the percentage of cells with a short cycle life (defined for < 50 cycles in this work) shows a significant decrease over iterations, from 80.6% for the initial random round to 28.1% after the third iteration, whereas the percentage of cells with a long cycle life (defined for >100 cycles) increases from 9.7% to 40.6% after the third iteration (Fig. 3b). This clearly shows the efficacy of our DAL approach for electrolyte exploration, even with the large measurement noise associated with Li0 experiments. As the iterations progress, DAL’s confidence in optimizing the long-life electrolyte increases as confirmed by statistical ranking of tested cells’ cycle life, and after three iterations, the explored long-life electrolytes sufficiently represent the parameter space (discussed in Supplementary Fig. 5).

We now further show the success of DAL from a microscopic scale. Figure 3c shows the evolution of the space that is grouped by the type of salts (as a representative). The electrolyte formulas for the first round are randomly selected with two replicate tests (first column in Fig. 3c) to generate an initial dataset for DAL model building. Through only one DAL iteration, some electrolytes (i.e., those containing LiTFSI and LiFSI) are identified as “potential candidates” (second column in Fig. 3c). Interestingly, the LiDFOB regions (red dot area, first column in Fig. 3c) were allocated with many resources for the first iteration, but much fewer after that, which indicates the high experimental uncertainty in this zone that requires careful validation. By learning and exploiting structural information of the parameter space, DAL avoids evaluating electrolytes with low estimated cell cycle life and directs more resources to the high-performance region. This is also confirmed by individually analyzing other components of the space (discussed in Supplementary Fig. 6). In all, 621 of 720 electrolyte formulas were never tested (Fig. 3c); that is, we spent 0.22 experiments per electrolyte formula on average (utilizing only 4.4% of resources if one assumes exhaustive testing of five parallel cells for each electrolyte). Note that the DAL repeatedly tested several formulas with high estimated cycle life to decrease uncertainties due to a large experimental measurement variability (e.g., top regions of the LiTFSI and LiFSI groups, Fig. 3c).

In retrospect, the optimization results revealed some overall knowledge patterns; for example, electrolytes containing LiPF6, LiDFOB, DMC, and with a high concentration of 5m salts were not favored in general, indicating a negative outcome and leading to their exclusion from further iterations (Fig. 3, Supplementary Fig. 6, and Supplementary Note 3). Indeed, as the literature has previously reported, electrolytes containing LiPF6 and DMC do not support stable operation of Li0 due to the persistent formation of SEI51, 52; this crucial information was apparently quickly captured by DAL.

We further validated the high efficacy of DAL by experimentally testing a subset of five electrolyte formulas identified with the highest cell lifespan recommended by DAL after the third iteration. We tested each of these electrolytes five times by cycling the cells until failure. The mean cycle life, calculated as a weighted average from these multiple tests, is considered an estimate of the true cycle life (Supplementary Note 4). The recommended top five electrolytes, all containing ether components, exhibit a longer lifespan with high reproducibility compared to the state-of-the-art electrolytes with similar components (Fig. 3d, the selection criterion in Supplementary Note 5)55, verifying the efficacy of the DAL approach for the electrolyte design of LMBs.

The DAL approach described above allows for the rapid exploration of a defined parameter space; however, being able to quantify the intercomponent correlations would further empower the establishment of general design principles and intelligent exploration of a potentially much larger parameter space. Conventional efforts on decoding correlations are at best qualitative, with limited testing data by variable-controlled experiments and repeated validations. Further, when analyzing the topological network of two-dimensional pairwise correlations (i.e., between two components), there can be substantial disagreement between the positive and negative messages on one specific correlation, making it hard to extract valuable information (discussed in Supplementary Fig. 7). It is thus challenging to holistically evaluate two-dimensional correlations due to the lack of experimental verification of the whole parameter space.

In contrast, the methodology proposed herein allows for a deeper understanding of the general design principles. We now develop a TSC technique (Method section) to quantify correlation information among components from the electrolyte formulas recommended by DAL (Fig. 4a). TSC is an efficient technique that converts categorical features into numerical features with minimal information loss54. Specifically, TSC addresses categorical features (e.g., the co-presence of DME and DOL) by substituting the category of the k-th electrolyte sample with a numeric feature equal to a target value. It estimates the expected target value (e.g., cell lifespan in this work) conditioned by the category (Method section). With the DAL iteration’s ability to globally represent the entire parameter space and to offer holistic outcome prediction, TSC allows us to statistically quantify the impact of a specific component correlation on cell lifespan (herein defined as average degree of interaction, ADI) (Method section). Utilizing TSC, the correlation between two components (two-dimensional) or among multiple components (multi-dimensional) can be quantified. The mapping plot in Fig. 4b depicts the evolution of component interactions captured by our DAL approach with different iterations, specifically highlighted by the color order from the initial to third iteration (details in Supplementary Data 2 and Supplementary Fig. 8). The transformation of the ADI values from a random distribution to an ordered pattern (Fig. 4b) shows that the DAL approach equipped with TSC quantification (DAL-TSC) enables systematic improvement in capturing component interactions as iterations progress. Further correlation analysis between experiment- and DAL-derived ADI values is discussed in Supplementary Fig. 9. Notably, the ADI value provides a statistical perspective for electrolyte chemistry, such as the literature-reported correlation of DME-LiFSI (ADI: 96) 55, 57 and the newly identified correlation of EC-DOL (ADI: 114), offering further insights into electrolyte design (Fig. 4c).

In fact, due to DAL’s rich representation of the entire electrolyte space, as we now show (Fig. 4c), the correlation quantification identified a broad range of knowledge. Using the two-dimensional interaction as an example, with the TSC-quantified data we assessed the impact of a specific pair of components on the cell lifespan. Figure 4d depicts the quantitative comparison of pairwise ADIs for various pairs of components, wherein each pixel represents a comparison between two pairs sharing a common element. A colored pixel indicates that the ADI value of the pair on the horizontal axis exceeds that of the vertical, with the color intensity reflecting the magnitude of this difference. We further analyzed the statistical significance of each pairwise comparison via hypothesis testing based on all available experimental data (quantified as p, Fig. 4d). This diagram therefore offers valuable insights for rational design if one aims to pair a specific component with another. Furthermore, ADI not only identifies prior knowledge (i.e. known correlation patterns found from prior reports; marked as red circles in Fig. 4d), but also uncovers new knowledge about previously unknown correlation patterns (detailed in Supplementary Note 6 and Supplementary Data 2). In these maps, the red circles in the colored pixels indicate agreement with established knowledge, while those outside indicate potential discrepancies. Our analysis shows that approximately 85% of previously reported correlations align with our DAL-derived knowledge, validating DAL’s ability to generate meaningful insights for electrolyte design, while remaining discrepancies reflect limited literature statistics and the DAL framework’s focus on interactions that enhance lifespan. The validity of this knowledge is shown by the zero-shot optimization as discussed later. Therefore, DAL-TSC demonstrates a much deeper understanding of the design principles than current literature reports, and we can follow these rules for rational design in a large parameter space. We also globally quantified the correlations among three components (detailed in Supplementary Fig. 11), which is beyond the capacity of conventional manual-based quantification methods. In fact, we speculate that the DAL approach can in principle quantify even higher-dimensional intercomponent correlations (Supplementary Fig. 12). This significantly expands the ability for in-depth exploration and autonomous design of more diverse electrolyte systems.

Commercial electrolytes typically contain multiple more than two solvents and additives at varying concentration ratios, creating a parameter space that is prohibitively complex and time-consuming to explore through exhaustive experimental testing. Using the DAL approach, which naturally captures the knowledge of electrolyte design including the reported prior knowledge, we can design electrolytes of higher orders of complexities in a notably more efficient manner by transferring the knowledge. Here, using the same chemical components as originally used and releasing some parameter constraints, we expanded the targeted parameter space from 720 to 5400 (Fig. 5a).

We now use the developed TSC method to integrate experimental data from the original parameter space into this expanded parameter space. TSC captures and encodes key knowledge of component correlations that can be shared between the original and the current electrolyte exploration tasks (Fig. 5a and Method). The knowledge gained on component correlations discussed above was then integrated into the DAL model, enabling it to learn the similarities and differences between these two tasks. The model can thus efficiently transfer the knowledge and generalize its inferences to this new electrolyte design problem (discussed in Supplementary Fig. 13). To demonstrate the success of electrolyte exploration within an expanded parameter space, we utilized the DAL approach in a zero-shot manner (i.e., a non-iterative training without performing any experimental testing). We repeatedly ran ten DAL optimizations, each recommending 32 high-performance electrolyte formulas through Thompson sampling. The times of recommendation for each recommended electrolyte formula were recorded (shown in Fig. 5b), from which we can identify electrolytes that are more likely to engender better Li0 reversibility.

Experimental validation was performed on the top five electrolytes recommended by DAL. The experimental results show that among these, four electrolytes achieved stable cell cycling for over 1800 hours (Supplementary Fig. 15). The cells using the four electrolytes reaching an average cycle life of 200.6 cycles (Fig. 5c), which is 1.6 times longer than the average lifespan of the original parameter space after iteration (Fig. 3a). The ability of DAL to rapidly optimize a large parameter space of 5400 in a short time and with fewer resources confirms its high efficiency in exploring complex electrolyte systems through capturing the component correlations, which will facilitate autonomous exploration of complex electrolyte systems and accelerated discovery of materials.

Practically, an advanced electrolyte must withstand both Li0 negative electrode and high voltage positive electrode simultaneously. The positive electrodes, particularly the aggressive high nickel-content oxides, often impose different, if not conflicting, requirements on the electrolytes and interphases, which means the design of a full cell envelops more interphasial reactions and thus may appear more challenging. Furthermore, the dynamically advancing discovery of new molecules in the field may continue to benefit electrolyte formula for the industry; integrating these new molecules into existing parameter space is important but may cause combinatorial explosion of the space. Here, the framework integrating DAL and TSC is expected to handle such challenges by actively learning the hidden component interactions and recommending high-performance electrolytes with only a small number of additional experimental tests, as illustrated in Fig. 6a and b.

Here, given that electrolytes’ stability with Li0 negative electrodes (evidenced by Li0||Li0 cell performance) is a prerequisite for achieving good cycling performance in full cells (detailed in Supplementary Fig. 16), we leveraged the knowledge captured by DAL for optimizing electrolytes for Li0||LMO full cells through few-shot optimization. The down-selected group of top 100 electrolytes (ranked during the Li0||Li0 cell optimization above) serves as the parameter space for Li0||LMO full cell optimization (Fig. 6a, detailed in Methods). The top 8 recommended electrolytes were prioritized for experimental testing in full cells employing a 50 μm-thick Li0 negative electrode paired with a LiNi0.8Co0.1Mn0.1O2 (NCM811) positive electrode (areal capacity: 2.03 mAh cm⁻2) using 1/3C charge/discharge protocol. The experimental data (100-cycle capacity retention, raw data shown in Supplementary Fig. 17) served as training inputs for subsequent TSC encoding (i.e. the expected target value is capacity retention) and DAL few-shot optimization, with the results shown in Fig. 6c. As a validation, the second-round recommended top 5 electrolytes delivered an average 100-cycle capacity retention of 84.0% (Fig. 6d, voltage profiles in Supplementary Figs. 17-18), substantially outperforming the 58.2% retention of the initial 8 electrolytes — a significant enhancement achieved with only one DAL iteration. This demonstrates the effectiveness of the DAL-TSC learning framework in knowledge transfer to optimization of the full-cell configuration.

Furthermore, to address the practical challenge of incorporating newly discovered molecules into existing parameter space which causes combinatorial explosion, we developed a few-shot optimization workflow under the DAL-TSC framework. As a proof of the concept, we included two recently reported molecules—1,2-diethoxypropane (DEP) as a solvent molecule and trioxane (TO) as an additive (19, 20)—and constructed a parameter space encompassing 5760 new electrolyte formulas. For TSC coding the initial ADIs of DEP-or TO-related interactions were assigned as the prior p, which corresponds to the mean values of existing interactions. One batch (32 electrolytes) of experimental cell testing was performed to serve as the input for the few-shot DAL optimization, and the top 32 recommended electrolytes were tested for validation (Fig. 6b, see Methods for details). Specifically, with a single-round experimental test of 32 DEP- and TO-containing electrolytes, the mean value of the cell capacity retention increases by 131% from 24.4% (first recommendation) to 56.5% (second recommendation) (Fig. 6e, Supplementary Tables 5-6). Note that here 150-cycle capacity retention was used in light of the generally improved performance with the new molecules. Specifically, the electrolyte formulated as 0.75m LiTFSI 0.75m LiFSI DME/EC/DEP+VTC/LiNO3 delivers 83% capacity over 250 cycles, which is greatly improved over the previous optimized electrolytes (i.e. 57.2% for 1.25 m LiTFSI+1.25 m LiFSI DME/EC/PC+FEC/LiNO3; Fig. 6f). This demonstrates that our DAL framework can effectively transfer previously acquired knowledge to guide electrolyte design involving newly introduced molecular components. By initializing unknown interactions with statistically derived priors and incorporating only a small number of experimental measurements, the framework dynamically expands the searchable space, enabling efficient optimization as new molecules are discovered without restarting the process.

Methods
Experimental
The electrolytes in this work were prepared with rigorous control of the content of water. All lithium salts (lithium hexafluorophosphate (LiPF6, 99.99%, Aladdin), lithium bis(trifluoromethanesulfonyl)imide (LiTFSI, 99.99%, Aladdin), lithium bis(fluorosulfonyl)imide (LiFSI), lithium difluoro(oxalato)borate (LiDFOB), LiNO3, 99.99%, Aladdin) were dried in a vacuum glass oven for 72 hours. The solvents (ethylene carbonate (EC, 99.99%, battery-grade, Aladdin), dimethyl carbonate (DMC, 99.99%, battery-grade, Aladdin), 1,2-dimethoxyethane (DME, 99.99%, battery-grade, Aladdin), 1,3- dioxolane (DOL, 99.99%, battery-grade, Aladdin), propylene carbonate (PC, 99.99%, battery-grade, Aladdin)) and additives (ethylene sulfite (ES, 99.99%, battery-grade, Aladdin), vinylene carbonate (VC, 99.99%, battery-grade, Aladdin) and fluoroethylene carbonate (FEC, 99.99%, battery-grade, Aladdin)) were treated with molecular sieves for over 96 hours to remove trace water. The electrolytes were then prepared based on the targeted formulas in an Ar glove box (<0.01 ppm H2O, <0.01 ppm O2). To prevent overheating, the salts and additives were added slowly at ambient temperature. After stirring and then standing respectively for 24 hours, the electrolytes are ready for assembling of cells. The algorithm-recommended electrolytes were used for cell measurements regardless of the color, states of dissolving, and any possible between-component reactions, as we deem the study as a non-expert process. To assemble the Li metal symmetric cells, two lithium metal disks of 18 mm in diameter and of 600 µm in thickness were used as the electrodes with a polyolefin separator (Celgard 2500 with Al2O3 coating, thickness: 25µm, porosity: 55%, Gurley value: 200s) in 2032-coin cell cases. For all cells, 50 µL of the electrolyte was used. The Li striping/plating cycling test was conducted with a current of 0.5 mA cm-2 for 4 hours discharge and 4 hours of charge at 25±0.05℃ in environmental chamber, with a voltage cut-off of 0.5 V.

For the fabrication of the full cells, positive electrodes coated with LiNi0.8Co0.1Mn0.1O2 (NCM811), purchased from Guangdong Canrd New Energy Technology Co., Ltd, China. (Model: SY31XX), were cut into 10 mm diameter pieces in an Ar glove box, and dried in a vacuum oven at 100 °C for 24 hours. The current collector was aluminium foil with a thickness of 12 μm and an areal density of 3.5 mg cm-2; the mass fraction of active material was 94.5%. The areal loading for the NCM811 positive electrodesis 10.8mg cm-2. For the lithium metal negative electrode, a fresh lithium foil without surface treatment (10 mm in diameter and 50 µm thick, Tianjin Tianneng Co., Ltd, China) was pressed onto a hydrogen-reduced copper foil (16 mm in diameter) to ensure good contact between the lithium and copper foils. To assemble the Li0||LMO full cells, the prepared positive electrodes, a polyolefin separator (Celgard 2500 with Al2O3 coating), and the Li/Cu negative electrode were assembled into 2032-coin cell cases, each containing 50 µL of electrolyte. The assembled full cells were tested at 25±0.05℃ using 1/3C charge/discharge protocol with a voltage window of 3.0 V-4.3 V.

Computational
Deep active learning: For electrolyte optimization, a deep kernel learning (DKL)-based active learning (AL) approach is proposed. AL is a Bayesian optimization-based machine learning approach for the global optimization of black-box objective functions that are noisy and expensive to evaluate49; this is the characteristics of the objective function to be optimized in the electrolyte design problem for lithium metal batteries (LMBs) in this study. Generally, AL comprises of a probabilistic surrogate model and an acquisition function, in which the surrogate model such as Gaussian process is used for approximating the expensive and noisy objective function, and the acquisition function is to sample-efficiently probe the parameter space by balancing exploration and exploitation50.

For probabilistic surrogate modelling, Gaussian process is commonly used and can be described by the mean and covariance function58. For the objective function f(x), its GP model can be described as

f(x)~GP(m(x),κ(x,x′)) (2)

where m(x) denotes the mean of the Gaussian process, and κ(x,x′) denotes the covariance function. In this work, the variable x is an electrolyte formula with certain solvents, lithium salts, salt concentration and additives, and f(x) models the mapping from an electrolyte formula x to the corresponding cell lifespan.

When the observation of the objective function is coupled with noise, that is

y = f(x)+ε (3)

where f(x) denotes the unknown true cycle life of the cell for a given electrolyte formula x, while the observed cycle life y is experimentally measured and contains uncertainty due to experiment noise ε, which we assume follows a normal distribution N(0,σ2). The posterior distribution predicted based on the GP, given a dataset D = {(x(i),y(i))}Ni=1, can be obtained as

p(y| D) = N(μ(x;D),σ2(x;D)) (4)

where

μ(x;D) = KT(x)(Σ +σ2I) -1 y (5)

σ2(x;D) = K(x,x)-KT(x)(Σ +σ2I) -1 K (6)

with K(x) = [κ(x,x(1)),…,κ(x,x(N))]T, and [Σ]i,j = κ(x(i),x(j)).

The selection of covariance function κ(⋅,⋅) is important for the GP model, which is to capture the similarity of any two data samples, and thereby specifies the smoothness or oscillation degree of the black-box objective function59. Selecting a suitable covariance function can largely enhance the modeling performance of GP. However, standard GP kernel functions such as radial basis function (RBF) kernel are found difficult to capture the non-stationary structure in a complex system such as the electrochemical operation of LMBs, and thereby deteriorate the performance of AL for the design of LMB electrolytes. To address this issue, GP based on DKL was utilized in our work which combines the representational power of deep neural network with the reliable uncertainty estimates of GP. The deep kernel7, 49 is defined as Eqn. (1) in the main text, and a variational inference algorithm57 was used to maximize the marginal likelihood function of DKL-GP to obtain its parameters.

For the acquisition function, a Thompson sampling (TS) strategy60 was employed to determine the next electrolyte formula x(t). In each iteration, TS draws a sample from the posterior predictive distribution p(y| Dt) and selects the formula that maximizes the outcome:

x(t) = argmaxh(x), h(x)~p(y| Dt) (7)

where Dt = {(x(i),y(i))}t-1 i=1 represents the history of evaluations. The selected electrolyte formula x(t) is then experimentally evaluated, yielding an observed cycle life y(t), and the dataset is updated as Dt+1 = Dt ∪ {(x(t),y(t))}. By iteratively sampling from the posterior predictive distribution, TS efficiently explores the electrolyte design space while balancing exploration and exploitation to accelerate the identification of optimal electrolyte compositions for extended cycle life.

Target statistics coding: Quantifying correlation information among electrolyte components requires transforming discrete categorical features (e.g., the co-presence of DME and DOL) into numerical representations. This transformation is essential for knowledge transfer between original and target electrolyte exploration tasks while facilitating efficient optimization. Target statistics coding (TSC) is an efficient method that converts categorical features into numerical features with minimal information loss. Specifically, TSC addresses categorical features by substituting the category of the k-th electrolyte sample with a numeric feature equal to a target statistic. Specifically, we encode the relational feature Xi of the electrolyte in the k-th sample as its expected component correlation value, which can be estimated as56:

φ(Xi(k)) = E(y|Xi = Xi(k)) = ΣNj=1 1{Xj(j) = Xi(k)} ⋅yj / ΣNj=1 1{Xj(j) = Xi(k)} (8)

where Xj represents the relational feature i in the j-th sample, y is the target value (i.e., cell lifespan or capacity retention in this work), and 1{ } is the indicator function.

Eqn. (8) shows that the expected correlation value for relational feature Xi is approximated as the average degree of interaction (ADI) across all electrolyte samples sharing the same relational feature as Xi(k). Since this estimation may be unreliable for low-frequency features, a prior p is introduced for smoothing, formulated as:

φ(Xi(k)) = λi ⋅E(y|Xi = Xi(k))+(1−λi)⋅p (9)

where p represents the average target value in the electrolyte dataset, and λi is a weighting factor defined as

λi = 1 / (1+exp(− ΣNj=1 1{Xj(j) = Xi(k)} −C / d)) (10)

Here, C and d are hyperparameters that control confidence and smoothing, respectively. Specifically, C represents the threshold number of samples required for a reliable estimation of the conditional mean, while d determines the degree of smoothing. This formula effectively balances empirical observations with prior knowledge, providing reliable estimates even for electrolyte relational features with limited experimental data points.

Average degree of interaction (ADI) and knowledge transfer: To effectively transfer knowledge across electrolyte optimization tasks, we utilize TSC to quantify key component correlations from the high-performing electrolyte formulas recommended by DAL in the first stage. These quantified relational features encompass pairwise, triplet, and higher-order correlation values, capturing the underlying interactions among the components. Specifically, for the k-th sample’s electrolyte formula composed of L distinct components, we represent its feature vector as:

X(k) = [ 〈xl(k) ,xs(k) 〉,…,〈x1(k) ,x2(k) ,…,xL(k) 〉], 1 ≤ l,s ≤ L (11)

where xl(k) represents the individual electrolyte formula feature l (e.g., lithium salt, solvent, additive, concentration) of the k-th sample; 〈x1(k) ,x2(k) ,…,xL(k) 〉 represents the (L-1)-th order relational features (i.e., the interactions among L components). These features are estimated by the expected target values (e.g., cell lifespan) within their respective categories, enabling us to quantify specific component interactions, defined as:

φ(X(k)) = [φ(〈xl(k) ,xs(k) 〉),… ,φ(〈x1(k) ,x2(k) ,…,xL(k) 〉)], 1 ≤ l,s ≤ L (12)

For example, the encoding for first-order relationships (i.e., φ(〈xl(k) ,xs(k) 〉)) can be estimated using Eqn. (7), which corresponds to the average cycle life across all electrolyte samples containing the corresponding relational feature 〈xl(k) ,xs(k) 〉 , or estimated by incorporating additional prior information as specified in Eqn. (9). This encoding quantifies the interaction between specific components, a metric we refer to as average degree of interaction (ADI). For instance, the average degree of interaction between the DOL and EC components yields an encoding value of approximately 113.7 cycles (i.e., ADI(〈DOL,EC〉) = φ(〈DOL,EC〉) = 113.7).

Once the feature vector is obtained, it serves as a comprehensive representation of electrolyte formulas, embedding key component correlation knowledge. In the second stage, this encoded numerical representation is used as input to the DAL framework over an expanded design space, enabling efficient knowledge transfer through two approaches: (1) To generalize the DAL framework in symmetric cells across a larger chemical space, the ADI features derived from experimental data within the initial parameter space were applied to the DAL framework in a zero-shot manner, enabling the recommendation of electrolyte formulas. (2) For generalization in full cells across a larger chemical space—and given that symmetric cell performance is a prerequisite for reliable full-cell cycling—we defined the Li0||LMO full-cell optimization space as the top 100 electrolyte formulas recommended by the Li0||Li0 cell optimization. This served as the starting point for the optimization process. Subsequently, TSC was employed to quantify the influence of relational features on capacity retention, and this quantification was used as input for the next iteration of DAL, facilitating few-shot optimization. (3) For the newly discovered molecules, their associated interactions (here, DEP- or TO-based interactions) were assigned a prior value p (i.e., the mean interaction value in the electrolytes), and DAL was applied in a zero-shot manner to recommend 32 electrolytes for experimental validation in full cells. The measured data obtained from these experiments was then used for the second iteration of DAL.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Hong et al., presents a sophisticated deep active learning framework to accelerate materials discovery. By integrating deep kernel learning with TSC, the authors have developed a two-stage AI framework that addresses a key challenge in the field by effectively exploring the discontinuous property landscapes of electrolytes. Critically, this framework can also dynamically incorporate new, advanced molecules into the optimization process without requiring a full restart. This AI framework is shown to substantially accelerate the identification of high-performance candidates within complex, multicomponent electrolyte systems.\nThis study is both timely and significant. It demonstrates a meaningful integration of experimental investigation with advanced machine learning methodologies, highlighting the importance of aligning algorithmic development with realistic experimental scenarios. The authors provide convincing experimental evidence that their framework mitigates key challenges arising from high chemical discontinuities and large experimental noise, thereby enhancing the reliability and efficiency of the electrolyte discovery process.\nOverall, this work represents a valuable contribution to the field of energy storage and will be of broad interest to researchers focused on electrolyte design and data-driven materials discovery. I endorse its publication in Nature Communications and provide the following comments to further strengthen the manuscript.\n1. During the knowledge transfer stage, ADI values were calculated to guide further electrolyte design via DAL. Could the authors elaborate on whether these values could also serve as practical indicators for electrolyte chemists, thereby enabling more rational and efficient electrolyte formulation?\n2. The electrolyte for lithium metal batteries needs to balance the stability of both the lithium metal anode and the cathode. The authors first evaluated lifespan in Li||Li symmetric cells and then extended the exploration to full-cell systems. Would direct application to full-cell configurations be feasible and potentially more efficient?\n3. The comparison between TSC-derived knowledge and reported results shows an 85% overlap, but also a 15% discrepancy. Will this discrepancy may influence the effectiveness of subsequent optimization strategies?\n4. While BO has been applied and discussed, there exist other promising optimization methods (e.g., PHOENICS or other global optimization algorithms). A brief discussion of alternative strategies may broaden the applicability and impact of the proposed framework.\n5. In repeated experimental results, such as those presented in Fig. 3D and Fig. 5C, the standard deviation of the measured lifetimes appears to be relatively large. The author should provide the reasons for such large deviation.\n6. In exploring a larger parameter space, the authors employed a broader range of components, including two types of salts, three types of solvents, and multiple additives, resulting in 5,400 different electrolyte combinations. What were the practical considerations behind this configuration?", "reviewer_2": "The study by Hong et al. presents a deep active learning (DAL) approach for optimization of electrolyte formulations for lithium metal battery (LMB) full cells using deep kernel learning (DKL). The approach was successfully used by the authors to find efficient electrolytes compared to initial electrolytes tested. The authors also developed a target statistic encoding (TSC) framework to quantify learned knowledge and then leverage it to find newer electrolytes with few-shot learning.\nThe present study provides certain advancements in the data-driven battery materials discovery field and carries out >100 real-world battery testing. However, there are significant limitations and loopholes in the developed approach that should be addressed to make it truly generalizable. Here are detailed comments:\n1. The manuscript revolves around the central idea that their approach can be utilized to perform optimization of electrolyte properties in the discrete electrolyte chemical space as they mentioned it multiple times in the introduction and elsewhere: “… these approaches have been confined to scenarios featuring a numerically continuous space.” However, some of the recent works have already been developed utilizing AL framework to carry out optimization of electrolytes in the discrete space, e.g., Noh et al., Nat Commun 15, 2757 (2024); Zhang et al., Mater. Today Energy 51, 101909 (2025). It should be clearly stated along with proper citations of these references. I have further reservations on their “optimization in discrete space” claim, which I will point out below.\n2. The authors also mention “large experimental variability” in reporting battery testing metrics such as cycle life, which is certainly true and is also apparent from Figures 3 and 5. So, I commend the authors for reporting such true and large variations in the manuscript, which is seldom reported in the literature. But my question is how to predict such large measurement noise, i.e., aleatoric uncertainties? A Bayesian technique such as DKL can be used to predict such aleatoric uncertainties, so the authors should check if their DKL model can indeed reproduce the noise in their measurements. It will be highly beneficial to the community.\n2. The authors did not open source their codes, which is one of the requirements of the journal. While they did provide access to their partial codebase, I would also need access to data, model checkpoints and remaining codes in order to ensure it is fully reproducible. The provided codebase is also not well-documented. So, I recommend that the authors upload all their codes, datasets, and model checkpoints on GitHub and/or Zenodo with detailed documentation on how to use it including the python libraries involved.\n3. Why choose Thompson sampling as acquisition function over standard and more common acquisition functions such as the expected improvement? There is no justification provided in the draft.\n4. The optimization is carried over only 13 molecular components (6 solvents, 4 salts, 3 additives) and later two more molecular components were added in the search space. While we know that molecular chemical space is enormous, estimated to be on the order of 1060. So, is their approach truly carrying out optimization over discrete electrolyte space then? The search space is also very small – 720, 5400 and 5726. Do we really need AL for such small spaces? AL is usually carried over large search spaces on the order of thousands, if not millions, of input samples. A frequentist ML model can well be utilized to find optimal candidates in such small search spaces.\n5. In Figure 2e, I believe the comparison between GP-AL and DAL is made using the RBF covariance kernel in GPs. While it is true that RBF is suited for smooth and continuous functions, there are also other standard covariance kernels that can be used when there is roughness in the functions, e.g., Matern, rational quadratic, pairwise, etc. Multiple covariance kernels can also be combined together to achieve the desired effect. So, their choice of using DKL over GP in the present study is not well justified. They should compare GPs with aforementioned covariance kernels to truly establish the superiority of DKL over GPs in such scenarios.\n6. Along the same lines, the authors mention that “…the black-box functions with rapid oscillations, which are characteristic of the objective function in the electrolyte optimization problem…” But it has not been explicitly shown that the objective function for electrolyte optimization problem is indeed “rapidly oscillating”.\n7. The authors also make claims about DAL framework being able to balance between exploration and exploitation. This can be explicitly shown on a reduced latent space representation of electrolytes from the trained DKL model by showing suggestions from different batches. If the model is indeed exploiting, then the suggestions from later batches should converge to a particular region of the chemical space. The authors can also show distribution of uncertainties for suggestions from different batches and if the model is progressing towards exploitation, then the distribution of uncertainties should shift towards lower values.\n8. How are the molecular components represented? I do not see any discussion in the Methods section. Do they represent molecules using Morgan fingerprints or RDKit features or graph neural networks (GNN) or some sort of one-hot encoding? If one-hot encoding is used to represent molecular components in the electrolytes, then their model cannot really be inferred on molecular components unseen by the DKL model. If that’s the case, then the claim of “optimization over discrete electrolyte space” again does not really hold true.\n9. I also have reservations about their developed TSC approach. The average degree of interaction (ADI) values from this TSC approach can only be obtained post training of the DKL model and is not learned during the training itself. This limits the utility of this approach. Also, continuing from previous point, one needs to know the ADI values of unseen molecules a priori in order to make predictions: “For TSC coding the initial ADIs of DEP-or TO-related interactions were assigned as the prior (cid:1), which corresponds to the mean values of existing interactions.” This will severely limit the applicability of their approach on finding electrolytes constituting unexplored solvent, salts, or additives, as one would need to first perform real-world experiments using these unexplored molecular components.\n10. Other non-technical comments:\na) The introduction section is a bit too long. Even though there is no word limit in the Nature Communications journal, I think it contains redundant information and so can be easily reduced to two-thirds.\nb) Some of the sentences are also too long and are hard to follow, e.g.:\n“To complicate it further, unlike the optimization of nonchemical (particularly numerical) subjects of interest – the examples of which include battery fast-charging protocols, and physical properties of electrolyte (solubility and concentration, ionic conductivities and viscosity) that vary over a continuous space of numbers – the materials space for electrolyte design is highly discrete, because the component-performance relationship is highly sensitive to many equilibria and inequilibria processes existing in the cell environment, such as the interphasial chemistry and related properties, where the change of a single chemical or its concentration may trigger an exponential increase in potential component interactions, resulting in the combinatorial explosion of search space.”\nc) Some of the words used in the draft can be replaced with more suitable ones, e.g., “recommendation” with “suggestion” since the word recommendation gives the idea that a recommendation system is being utilized to get new suggestions in each batch, which is not the same as an AL framework.\nb) Add a separate “Discussion” section in the revised draft (which is allowed as per journal’s guidelines) clearly highlighting limitations of their approach as pointed out above.", "reviewer_3": "The author describes a deep active learning approach to discover new electrolytes for lithium metal batteries. Overall, the work is well structured and clearly presented. I believe that the novelty lies in the combination of deep learning and active learning. However, the author primarily focuses on convincing readers of the importance of this technique for improving the efficiency of electrolyte screening for lithium metal batteries. The main conclusions of the work appear somewhat scattered. I suggest that the author highlight the key novelty of the study more explicitly. I have some concerns for the author to consider, listed below:\n1.The work illustrated in the paper is too specific, and I can imagine that the author spent substantial time completing the experiments. How, then, can the author convince us that this method truly reduces time costs?\n2.The performance of lithium metal batteries is important; however, it is still not sufficient to represent or transfer the overall performance to other devices. Thus, the experimental design is critical. LMO is not a typical cathode for lithium metal batteries—why not use NCM cathodes for validation?\n3.The authors need to emphasize the importance and necessity of DKL and Thompson sampling by comparing them with the standard BO process.\n4.Overall, I think this work is highly interdisciplinary. Researchers from the battery field and the machine learning field could easily become confused. Therefore, integrating the two effectively will be a major challenge for the authors to address in order to improve the work."}, "author_response": "Response Letter to Reviewers’ Comments on Manuscript\nNCOMMS-25-60533\nWe thank the reviewers for their valuable comments. In response, we further elaborated on the\ndetails of the algorithm, provided explanations regarding data noise, reliability, and the design\nof the two-stage optimization framework, as well as made textual technical modifications to\nenhance the logicality and readability, diligently addressed each comment and incorporated the\nsuggestions into the revised manuscript (major changes highlighted in red for clarity), as\nexplained below in detail. Answers to the reviewers’ comments are presented in blue type, while\na portion of the updates to the manuscript and Supplemental Information are copied here and\nmarked in red.\nReviewer #1 (Remarks to the Author):\nThe manuscript by Hong et al., presents a sophisticated deep active learning framework to\naccelerate materials discovery. By integrating deep kernel learning with TSC, the authors have\ndeveloped a two-stage AI framework that addresses a key challenge in the field by effectively\nexploring the discontinuous property landscapes of electrolytes. Critically, this framework can\nalso dynamically incorporate new, advanced molecules into the optimization process without\nrequiring a full restart. This AI framework is shown to substantially accelerate the identification\nof high-performance candidates within complex, multicomponent electrolyte systems.\nThis study is both timely and significant. It demonstrates a meaningful integration of\nexperimental investigation with advanced machine learning methodologies, highlighting the\nimportance of aligning algorithmic development with realistic experimental scenarios. The\nauthors provide convincing experimental evidence that their framework mitigates key\nchallenges arising from high chemical discontinuities and large experimental noise, thereby\nenhancing the reliability and efficiency of the electrolyte discovery process.\nOverall, this work represents a valuable contribution to the field of energy storage and will be\nof broad interest to researchers focused on electrolyte design and data-driven materials\ndiscovery. I endorse its publication in Nature Communications and provide the following\ncomments to further strengthen the manuscript.\nOur Response: We sincerely thank the reviewer for the positive evaluation of our work on\nintegrating deep active learning with TSC for accelerated electrolyte discovery. As highlighted,\nour framework was specifically designed to address key practical challenges in electrolyte\ndevelopment, including the discontinuous property landscape, substantial experimental noise,\nand the dynamic incorporation of new molecules. By adopting a two-stage deep active learning\nstrategy, we achieved efficient and reliable optimization in complex multicomponent electrolyte\nsystems, as further validated by our experimental results. We also hope this framework can\n1\nattract broader attention from researchers and help speed up the development of electrolytes\nand other materials.\n1. During the knowledge transfer stage, ADI values were calculated to guide further electrolyte\ndesign via DAL. Could the authors elaborate on whether these values could also serve as\npractical indicators for electrolyte chemists, thereby enabling more rational and efficient\nelectrolyte formulation?\nOur Response: Thank you for this valuable comment. The ADI value is a statistical measure\nthat links electrolyte formulations with their estimated outcomes in the parameter space. It\nreflects the overall interaction among components with respect to LMA stability. While it\ncannot serve as a direct chemical descriptor like solvent polarity, it captures the combined effect\nof different components. We therefore believe ADI values can help connect electrolyte\ncomposition to the resulting lithium metal performance. For example, as discussed in the\nmanuscript, the ADI value of 96 for DME-LiFSI reflects the known stabilizing role of DME\ntogether with inorganic SEI formation from FSI− decomposition, whereas the higher ADI value\nof 114 for EC-DOL suggests the stabilizing effect of DOL on carbonate-based electrolytes. We\nhave now added further discussion in the manuscript on the potential of ADI as a practical\nindicator for electrolyte chemistry.\nWe have now added the discussion to the manuscript as:\nNotably, the ADI value provides a statistical perspective for electrolyte chemistry, such as the\nliterature-reported correlation of DME-LiFSI (ADI: 96) and the newly identified correlation of\nEC-DOL (ADI: 114), offering further insights into electrolyte design.\n2. The electrolyte for lithium metal batteries needs to balance the stability of both the lithium\nmetal anode and the cathode. The authors first evaluated lifespan in Li||Li symmetric cells and\nthen extended the exploration to full-cell systems. Would direct application to full-cell\nconfigurations be feasible and potentially more efficient?\nOur Response: The discontinuous nature of electrolyte properties exists in both Li||Li\nsymmetric cells and full-cell system. Therefore, our DAL method which targets discontinuous\nstructure-property landscapes, can in fact be applied directly to full-cell electrolyte discovery.\nAs shown in our few-shot optimization experiments with full-cells, our two-stage framework\nalso demonstrates efficient exploration. In practice, especially for industrial applications where\nfull-cell performance is of primary concern, electrolyte formulations and full-cell performance\ndata can indeed be directly integrated into our framework for optimization. However, as you\nnoted, the stability of both the lithium metal anode and the high-voltage cathode must be\n2\nconsidered simultaneously. For this reason, in our current study we first separated the problems\nfor clarity, using symmetric cells as a demonstrative case. This allows the optimization process\nand the DAL-TSC framework to be better understood, while still being extendable to full-cell\ndesign.\n3. The comparison between TSC-derived knowledge and reported results shows an 85% overlap,\nbut also a 15% discrepancy. Will this discrepancy may influence the effectiveness of subsequent\noptimization strategies?\nOur Response: Thank you for this valuable comment. To further verify the validity of ADI\nvalues in electrolyte design, we compared our DAL-derived results with literature-reported\nelectrolytes that have similar component structures. Since the literature data and our ADI values\nare independent—and the reported studies often differ in testing methods and conditions—\nsome inconsistencies in component interactions are observed (as noted in Supplementary Data\n2) and were not included in the DAL comparison sequences. The 85% agreement indicates\nstrong consistency between literature statistics and ADI values, while the 15% discrepancy\nmainly arises from the limited number of statistically meaningful sequences in the literature\nand from the design of the DAL reward function. Specifically, DAL allocates higher precision\nto high-ADI interactions (which favor longer lifespan) and lower precision to low-ADI\ninteractions, thereby balancing accuracy and sample efficiency. As shown in Fig. 4d, this\nstrategy strengthens the certainty of high-ADI interactions during iterations, so the 85% overlap\nis reasonable and does not undermine the overall exploration efficiency.\nWe have now added the discussion to the manuscript as:\nOur analysis shows that approximately 85% of previously reported correlations align with our\nDAL-derived knowledge, validating DAL’s ability to generate meaningful insights for\nelectrolyte design, while remaining discrepancies reflect limited literature statistics and the\nDAL framework’s focus on interactions that enhance lifespan.\n4. While BO has been applied and discussed, there exist other promising optimization methods\n(e.g., PHOENICS or other global optimization algorithms). A brief discussion of alternative\nstrategies may broaden the applicability and impact of the proposed framework.\nOur Response: Thank you for your comment. While various optimization strategies exist,\nincluding Bayesian optimization frameworks like PHOENICS that you mentioned, PSO\n(Particle Swarm Optimization) and CMA-ES (Covariance Matrix Adaptation Evolution\nStrategy), they typically handle discontinuous variables through continuous relaxation (e.g.,\nassigning percentages to discrete salt choices) or encoding schemes (e.g., binary variables for\n3\nall possible combinations). Such encoding approaches significantly increase the dimensionality\nof the optimization space, making it challenging to achieve effective optimization with limited\nexperimental samples. Such approaches often increase the dimensionality of the search space\nand make optimization with limited experimental data less effective. PHOENICS, for example,\nachieves efficient optimization in high-dimensional continuous spaces via Bayesian kernel\ndensity estimation. However, the dynamic nature of electrolyte discovery requires an\noptimization method that can also perform transfer learning, so that newly introduced\nmolecules can be integrated without discarding accumulated knowledge.\nOur two-stage optimization framework addresses these challenges by combining deep\nactive learning with knowledge transfer. This allows efficient exploration of discontinuous and\ncomplex electrolyte spaces, reduces experimental cost, and enables adaptive incorporation of\nnew candidate molecules while retaining historical insights. As a comparison, we also applied\nconventional Bayesian optimization (GP-AL) with the same encoding scheme. Trained on the\nsame randomly selected batches, GP-AL did not significantly improve cycle life (Fig. R1,\nSupplementary Fig. 3e). In contrast, our deep kernel learning-based approach operated\neffectively in the discrete space and captured complex discontinuities, resulting in a clear\nimprovement in lifespan. This enhanced modeling capacity makes our framework especially\nvaluable in data-limited experimental scenarios.\nFig. R1. The experimental validation to compare the DAL and GP-AL methods. Randomly\nselected data were used as training data for both methods. The experimental electrolytes\nrecommended by the DAL approach (blue) exhibited a higher lifespan compared to those from\nthe GP-AL approach (orange). Inset: statistical result.\nWe have now added the discussion to the manuscript as:\nCompared with the standard Gaussian process-based active learning (GP-AL), our DAL\napproach can build a more accurate surrogate model for such a rapidly oscillating objective\nfunction (Fig. 2e and Supplementary Fig. 3), as further validated by experimental results\n(Supplementary Fig. 3e).\n4\nefil\nelcyC\n3\n3\n2\n2\n1\n1\n5\n0\n5\n0\n5\n0\n5\n0\n0\n0\n0\n0\n0\n0\n0\nefil\nelcyC\n3\n2\n2\n1\n1\n0\n5\n0\n5\n0\nV\nV\n0\n0\n0\n0\n0\n0\n0\naaa\n5\nn d\nlid\nlid\noaa\nE\nmtio\ntio\nle\ns e le c tio n\nn fr o m D A L\nn fr o m G P -\nM\n1 0 1 5\nc tr o ly te r a n k\nb a s e d A\nean value\n2 0\ne d b y c y\nL\nc le\n2 5\nlife\n3 0\n5. In repeated experimental results, such as those presented in Fig. 3D and Fig. 5C, the standard\ndeviation of the measured lifetimes appears to be relatively large. The author should provide\nthe reasons for such large deviation.\nOur response: We appreciate the reviewer for pointing out this important point. We note that\nthe measurement noise, i.e. the large standard deviation, reflects one of the main features of our\nDAL method which is to deal with large experimental errors over optimization. The possible\nreasons are:\n1) Variations of the potential profiles:\nFig. R2 shows a particular case of high data variability: the potential-capacity profiles of\n5 repeated Li0|Li0 symmetric cells using the same electrolyte. Cells A and B clearly exhibit soft\nshort-circuits, while Cell E experiences a hard short-circuit, i.e. a sudden drop of the\noverpotential. This difference should arise mainly from the unevenness of LMA surface, which\ncan lead to localized dendritic growth at specific points.\n-\n2\n2\n0\n0\n0\n0\n.\n)\nsv V( -2\n20\n0\n0\n60 70 80\nCycle time (hour)\n+iL )\n/iL -\n2\n2\n0\n0\n0\n0\n.\n)\nsv V( -2\n20\n0\n1\n0\n0 0\n410 1420 1430\n.s Cycle time (hour)\nv Cell C\nV\n( la itn e -\n2\n2\n0\n0\n0\n0 0\nlaitnetoP +iL/iL\n.\n)\nsv V( -2\n20\n0\n0\n0 0\nto 1520 1530\nP Cycle time (hour)\nCell D\n-\n2\n2\n0\n0\n0\n0\n0\nlaitnetoP +iL/iL\n.\n)\nsv\nV( -2\n20\n0\n0\n0\n0\n1540 1550 1560\nCycle time (hour)\nCell E\n200\n-20\n0\n0\nlaitnetoP +iL/iL\n.\n)\nsv V( -2\n20\n0\n0\n0 0\n1870 1880 1890\n0 500 1000 1500 2000 Cycle time (hour)\nCycle time (hour)\nFig. R2. The detailed voltage profiles for the validating electrolyte (1m LiDFOB\nDME/ES+5wt.% FEC) with five repeated cells. The red circles indicate short-circuit.\n2) Variations of laboratory experimental conditions:\nCell performance measurement variability is a particular challenge for laboratory\nexperiments. For example, even for testing of commercial cylinder batteries, the variability is\nalso large (e.g. Nature, 578, 397, 2020; Fig. R3). In our work, we have included all generated\ndata, which vividly shows the variability inherent in these tests.\n5\n[Figure Redacted]\nWe have now added the discussion to the manuscript as:\nEven when the training samples are deliberately assigned with large noise, generally arising\nfrom minor differences and large errors in lithium metal anode in experiments, the DAL\napproach efficiently identifies the optimal solution as early as the second iteration\n(Supplementary Fig. 4).\n6. In exploring a larger parameter space, the authors employed a broader range of components,\nincluding two types of salts, three types of solvents, and multiple additives, resulting in 5,400\ndifferent electrolyte combinations. What were the practical considerations behind this\nconfiguration?\nOur response: In principle, the composition of electrolytes can be expanded almost infinitely.\nIn industrial practice, the variety of lithium salts and primary solvents is usually limited to\naround 6-8 options, largely due to considerations of product consistency and manufacturability.\nIn our demonstration study, the initial parameter space was intentionally constrained to a single\nlithium salt, two solvents, and either one or no additive, in order to enable rapid optimization\nwith DAL. In subsequent investigations of larger parameter spaces, we expanded the number\nof lithium salts, solvents, and additives to better reflect practical application requirements.\nWe have now added the discussion to the manuscript as:\nCommercial electrolytes typically contain multiple more than two solvents and additives at\nvarying concentration ratios, creating a parameter space that is prohibitively complex and time-\nconsuming to explore through exhaustive experimental testing.\nReviewer #1 (Remarks on code availability):\nOur response: Thank you for this positive feedback. We are pleased that the provided code\nenables successful reproduction of the main results.\nThe study by Hong et al. presents a deep active learning (DAL) approach for optimization of\nelectrolyte formulations for lithium metal battery (LMB) full cells using deep kernel learning\n(DKL). The approach was successfully used by the authors to find efficient electrolytes\ncompared to initial electrolytes tested. The authors also developed a target statistic encoding\n(TSC) framework to quantify learned knowledge and then leverage it to find newer electrolytes\nwith few-shot learning.\nThe present study provides certain advancements in the data-driven battery materials discovery\nfield and carries out >100 real-world battery testing. However, there are significant limitations\nand loopholes in the developed approach that should be addressed to make it truly generalizable.\nHere are detailed comments:\nOur response: Thank you for your valuable comments that largely help improve the quality of\nour manuscript. Below we provide point-by-point responses that clarify challenges of\nexperiment-driven electrolyte optimization, expand on algorithmic details, and supply\nadditional data and analyses requested. We believe these revisions strengthen the manuscript\nand address the reviewer’s concerns.\n1. The manuscript revolves around the central idea that their approach can be utilized to perform\noptimization of electrolyte properties in the discrete electrolyte chemical space as they\nmentioned it multiple times in the introduction and elsewhere: “… these approaches have been\nconfined to scenarios featuring a numerically continuous space.” However, some of the recent\nworks have already been developed utilizing AL framework to carry out optimization of\nelectrolytes in the discrete space, e.g., Noh et al., Nat Commun 15, 2757 (2024); Zhang et al.,\nMater. Today Energy 51, 101909 (2025). It should be clearly stated along with proper citations\nof these references. I have further reservations on their “optimization in discrete space” claim,\nwhich I will point out below.\nOur response: We thank the reviewer for the comment. As you rightly pointed out, optimization\nof multi-component electrolytes inherently involves two dimensions: (i) the selection of\nmolecular components, which is discrete in nature, and (ii) the adjustment of their ratios, which\ncan be treated as a continuous variable. In the works cited by the reviewer (Noh et al., Nat.\nCommun. 15, 2757, 2024; Zhang et al., Mater. Today Energy 51, 101909, 2025), both aspects\nwere recognized, but the emphasis was primarily placed on continuous ratio tuning.\n⚫ Noh et al., Nat. Commun. 15, 2757, 2024: The parameter space was constructed from\nbinary solvent mixtures across continuous volume fractions, resulting in ~2000\nformulations derived from 22 molecular solvents. Because their input data were obtained\n8\nfrom a computationally accessible database, the Gaussian process-based active learning\n(GP-AL) approach was suitable and effective for ratio optimization. However, in\nexperimentally expensive domains such as ours, we found that GP-based methods are less\nrobust when faced with strongly discontinuous property variations, whereas the DAL\nframework offers superior adaptability.\n⚫ Zhang et al., Mater. Today Energy 51, 101909, 2025: The optimization variables were the\nmolar ratios of LiFSI:DME (X ) and LiFSI:TTE (X ), which are continuous in nature. As\n1 2\nalso confirmed in our Supplementary Figs. 2d-f, properties such as ionic conductivity\nand viscosity typically vary smoothly with concentration, making GP-AL an appropriate\ntool in such cases.\nIn contrast, our work focuses on the discrete molecular selection problem, where the\nchoice of individual components often leads to dramatic variations in electrolyte performance.\nWe have now cited these relevant works in the revised manuscript and clarified this distinction.\nMoreover, our experimental results demonstrate that standard GP-AL methods, which are better\nsuited for continuous spaces, are less effective when applied to this discrete molecular\noptimization problem, thereby underscoring the necessity of our DAL approach (Fig. R4.).\nFig. R4. The experimental validation to compare the DAL and GP-AL methods. Randomly\nselected data were used as training data for both methods. The experimental electrolytes\nrecommended by the DAL approach (blue) exhibited a higher lifespan compared to those from\nthe GP-AL approach (orange). Inset: statistical result.\nWe have now added these references to the manuscript:\n17. Noh, J. et al. An integrated high-throughput robotic platform and active learning\napproach for accelerated discovery of optimal electrolyte formulations. Nat. Commun. 15,\n9\nefil\nelcyC\n3\n3\n2\n2\n1\n1\n5\n0\n5\n0\n5\n0\n5\n0\n0\n0\n0\n0\n0\n0\n0\nefil\nelcyC\n3\n2\n2\n1\n1\n0\n5\n0\n5\n0\nV\nV\n0\n0\n0\n0\n0\n0\n0\naaa\n5\nn d\nlid\nlid\noaa\nE\nmtio\ntio\nle\ns e le c tio n\nn fr o m D A L\nn fr o m G P -\nM\n1 0 1 5\nc tr o ly te r a n k\nb a\ne a n\ne d\ns e d A\nva lu e\n2 0\nb y c y\nL\nc le\n2 5\nlife\n3 0\n2757 (2024).\n38. Zhang, J. et al. Dual-objective optimization of lithium metal battery electrolytes via\nmachine learning. Mater. Today Energy 51, 101909 (2025).\n2. The authors also mention “large experimental variability” in reporting battery testing metrics\nsuch as cycle life, which is certainly true and is also apparent from Figures 3 and 5. So, I\ncommend the authors for reporting such true and large variations in the manuscript, which is\nseldom reported in the literature. But my question is how to predict such large measurement\nnoise, i.e., aleatoric uncertainties? A Bayesian technique such as DKL can be used to predict\nsuch aleatoric uncertainties, so the authors should check if their DKL model can indeed\nreproduce the noise in their measurements. It will be highly beneficial to the community.\nOur response: We thank the reviewer for this insightful comment and for highlighting the\nimportance of reporting large experimental variability. We agree that this aleatoric uncertainty\nis an inherent and critical aspect of battery research that warrants more attention.\nThe central design principle of our work is to accelerate materials discovery via Bayesian\nframework. Consequently, its primary function is to efficiently guide the search for high-\nperforming electrolyte formulations rather than to explicitly model or reproduce the statistical\ndistribution of the experimental noise.\nNevertheless, aleatoric uncertainty is implicitly managed within our Gaussian process with\ndeep kernel learning (GP-DKL) approach. The GP-DKL surrogate models the predictive\nposterior distribution over the design space, and its variance term inherently captures the\nuncertainty associated with its predictions. Our Thompson sampling-based acquisition function\nleverages this full posterior distribution—not just the mean prediction—to balance exploration\nand exploitation. By sampling from the surrogate, the algorithm naturally accounts for regions\nof high uncertainty, which are influenced by both a lack of data (epistemic uncertainty) and\ninherent measurement noise (aleatoric uncertainty). This optimization-focused approach is\nparticularly well-suited to our application context, where experimental evaluation of electrolyte\nperformance presents significant challenges: each sample requires ~3 months of testing time\nand is subject to considerable experimental variability.\nWe agree with the reviewer that a direct assessment of the DKL model’s capability to\nreproduce the observed aleatoric uncertainty would be a valuable contribution and an\ninteresting direction for future research. However, for the specific objective of this work—\naccelerated optimization under severe experimental constraints—the key performance metric\nis the efficiency of discovering optimal candidates. Therefore, the success of our framework is\nbest measured by its demonstrated ability to rapidly identify promising electrolyte formulations\nwith minimal experimental overhead, as shown through our active learning iterations and the\n10\nsuccessful knowledge transfer.\n2. The authors did not open source their codes, which is one of the requirements of the journal.\nWhile they did provide access to their partial codebase, I would also need access to data,\nmodel checkpoints and remaining codes in order to ensure it is fully reproducible. The provided\ncodebase is also not well-documented. So, I recommend that the authors upload all their codes,\ndatasets, and model checkpoints on GitHub and/or Zenodo with detailed documentation on how\nto use it including the python libraries involved.\nOur response: Thank you for your comment. All the codes and datasets have been uploaded to\nGitHub (https://github.com/XWang1999/Electrolyte_Optimization_Deep_Active_Learning)\nwith detailed documentation specifying the Python library dependencies and step-by-step\ninstructions for reproducing the optimization workflow.\n⚫ Our framework is designed as an online optimization process that operates in tandem with\nsequential experimental measurements, where each experimental iteration informs the next\ncandidate selection. Accordingly, the released repository includes a demonstration\nnotebook (Electrolyte_Optimization_Demo_DAL.ipynb) that reproduces the full\noptimization workflow using three active learning iterations, providing a transparent and\nexecutable example of how the method operates in practice.\n⚫ The Deep Kernel Learning (DKL) implementation is provided in the dknet folder, which\ndetails the construction and training of the hybrid neural network–Gaussian process\nsurrogate. In addition, a numerical example implemented in DAL_numerical_demo.py\nillustrates the optimization process on a benchmark test function, offering a clear\ndemonstration of how the DKL-based surrogate performs iterative learning and guides the\nsearch toward optimal regions.\n⚫ For optimization in expanded parameter spaces, the framework can be directly extended\nby modifying the Target Statistic Coding (TSC) module according to the annotations and\nexplanations provided in the notebook. This procedure enables knowledge transfer\nbetween tasks and has been explicitly described in both the manuscript and the released\ncode, ensuring that the workflow can be readily adapted for broader electrolyte design and\nrelated optimization scenarios.\n3. Why choose Thompson sampling as acquisition function over standard and more common\nacquisition functions such as the expected improvement? There is no justification provided in\nthe draft.\nOur response: We selected Thompson Sampling (TS) over standard acquisition functions like\nExpected Improvement (EI) primarily for its superior and more straightforward scalability for\n11\nbatch-parallel Bayesian Optimization [R1]. This is a critical requirement by our experimental\nhardware.\nOur experimental platform is a 32-channel battery cycler, which allows us to test 32 distinct\nelectrolyte formulations simultaneously. To fully leverage this capability and accelerate the\noptimization process, we need select a diverse and promising batch of candidates at each\niteration, rather than a single point.\nThompson Sampling is well-suited for this batch scenario. To generate a batch of 𝑘\ncandidates (in our case, 𝑘=32), we can simply draw 𝑘 independent function samples from the\nposterior of the Gaussian Process surrogate model. The location of the maximum of each\nsample is then chosen as a candidate for the batch. This procedure is computationally efficient\nand naturally promotes exploration and diversity within the batch, as each sample represents a different\nplausible hypothesis of the true objective function.\nIn contrast, extending acquisition functions like EI to the batch setting is more complex. A naive\napproach of simply selecting the top 𝑘 points with the highest EI values would result in a\nhighly redundant batch, with points clustered around a single peak in the acquisition function.\nMore sophisticated methods like q-Expected Improvement (q-EI) are required to properly\naccount for the joint improvement over a batch, but they come at a much higher computational\ncost and implementation complexity [R2].\nGiven our experimental constraint of performing 32 parallel evaluations, Thompson Sampling\nprovides an elegant, scalable, and effective solution for maximizing the efficiency of our\ndiscovery workflow.\nTo improve the justification, the text below has been inserted into the “Deep active\nlearning approach” Section of the revised manuscript: “To fully leverage the experimental\nthroughput of parallel evaluations, an acquisition function of Thompson Sampling (see\nMethods) is then constructed based on the posterior distribution from the surrogate model of\nDKL. This strategy enables scalable batch-parallel optimization and efficiently sample the\nparameter space of electrolyte formulas by balancing exploration (i.e., testing regions with high\nuncertainty) and exploitation (i.e., testing promising regions based on completed experiment\nresults) 50”\n[R1] Kandasamy, K. et al. Parallelised Bayesian optimisation via Thompson sampling.\nInternational Conference on Artificial Intelligence and Statistics. 133-142 (2018).\n[R2] Gelbart, M.A. Constrained Bayesian Optimization and Applications. Harvard University,\n2015.\n12\n4. a) The optimization is carried over only 13 molecular components (6 solvents, 4 salts, 3\nadditives) and later two more molecular components were added in the search space. While we\nknow that molecular chemical space is enormous, estimated to be on the order of 1060. So, is\ntheir approach truly carrying out optimization over discrete electrolyte space then?\nOur response: Thank you for this important question, which touches on a crucial distinction.\nThe reviewer is correct that the universal molecular chemical space is astronomically large. Our\nwork, however, is not designed to address that molecular generative space. Instead, it targets\nthe formulation compositional space, which is a practical and important challenge in\nexperimental battery research.\nThis compositional space arises from the combinatorial mixing of a pre-selected set of\nviable components (solvents, salts, and additives). The primary bottleneck here is not\ncomputational but experimental. Each data point—representing a single electrolyte\nformulation—requires complex cell assembly, pre-conditioning, and months-long cycling tests\nto evaluate performance. Furthermore, these battery-level evaluations suffer from significant\nexperimental noise, where identical formulations can yield considerable variations in cycle life.\nBecause of this extreme cost and inherent variability, typical experimental studies report only\na handful of formulations.\nWhile our initial set of 13 components is modest, it generates a combinatorial space of\nover 5,400 unique formulations—a number far too large to screen exhaustively via brute-force\nexperimentation. The addition of just two new components expands this space beyond 10,000,\ndemonstrating the combinatorial explosion that necessitates an intelligent search strategy. Our\nframework was specifically developed to navigate this discrete, noisy, and expensive-to-\nevaluate space, providing a practical bridge between theoretical chemistry and real-world\nexperimental constraints.\nb) The search space is also very small – 720, 5400 and 5726. Do we really need AL for such\nsmall spaces? AL is usually carried over large search spaces on the order of thousands, if not\nmillions, of input samples.\nOur response: We agree with the reviewer that these search spaces are not large in a “big data”\ncontext. However, the need for Active Learning (AL) in our work is dictated not by the absolute\nsize of the search space, but by the prohibitive cost of each experimental evaluation.\nIn this domain, our total “experimental budget” is severely limited. Each sample requires\nmonths of testing and occupies a channel on our specialized equipment. Therefore, our primary\nobjective is to achieve maximum sample efficiency—to locate the optimal formulation in the\nfewest possible experimental steps.\nhigh query cost, where it intelligently selects the next most informative experiment to run. By\nsequentially learning and updating its model of the landscape, it minimizes the number of costly\nevaluations needed to converge on a high-performing candidate. The goal is not to exhaustively\nsearch the space, but to find the optimum with a budget of just a few dozen experiments. Our\ntwo-stage framework further enhances this by allowing the incorporation of new molecules\nwithout restarting the entire process, directly addressing a key limitation in practical research.\nThus, the use of AL is not only justified but essential for making progress in a field\nconstrained by such severe experimental bottlenecks.\nc) A frequentist ML model can well be utilized to find optimal candidates in such small search\nspaces.\nOur response: While a frequentist ML model could certainly be trained on a completed dataset\nto predict performance, it is fundamentally the ill-suited tool for the task of sequential\nexperimental design, which is the core of our work.\nThe critical distinction is that a standard frequentist model provides a point estimate (a\nsingle predicted value), but it lacks a measure of its own predictive uncertainty. In a data-\nscarce and expensive discovery campaign like the electrolyte discovery problem, this\nuncertainty is arguably more important than the prediction itself. It is the uncertainty that\nanswers the most crucial question: “Which experiment should I run next to find the\noptimum most efficiently?”\nOur Bayesian active learning framework is designed to answer exactly that question. By\nmaintaining a full posterior distribution, it quantifies the model’s confidence across the entire\nsearch space. This uncertainty is fed into our Thompson sampling acquisition function, which\nnaturally balances two critical needs:\n• Exploration: Testing in regions where the model is uncertain but the potential could\nbe high.\n• Exploitation: Refining candidates in regions already known to be promising.\nA frequentist model, lacking this uncertainty, cannot perform this intelligent exploration\nand would resort to a purely exploitative or random search, leading to lower sample efficiency\nand a higher risk of converging to a local optimum. Therefore, we chose a Bayesian approach\nnot just as a preference, but as a necessity for enabling the sample-efficient, guided search\nrequired to solve this problem with high cost of each experiment.\n5. In Figure 2e, I believe the comparison between GP-AL and DAL is made using the RBF\ncovariance kernel in GPs. While it is true that RBF is suited for smooth and continuous\n14\nfunctions, there are also other standard covariance kernels that can be used when there is\nroughness in the functions, e.g., Matern, rational quadratic, pairwise, etc. Multiple covariance\nkernels can also be combined together to achieve the desired effect. So, their choice of using\nDKL over GP in the present study is not well justified. They should compare GPs with\naforementioned covariance kernels to truly establish the superiority of DKL over GPs in such\nscenarios.\nOur response: We thank the reviewer for the comment and agree that the choice of covariance\nkernel critically affects the performance of Gaussian process (GP) models. In Figure 2e, the\nbaseline GP-AL results were shown with the radial basis function (RBF) kernel, which is a\nstandard default due to its smoothness assumptions and wide use in Bayesian optimization.\nImportantly, our comparison was not restricted to this case. In additional numerical studies, we\nexplicitly tested GP models with alternative kernels, including the Matern class, as reported in\nSupplementary Figs. 3 and 4. While Matern kernels provided some improvement over RBF\nin certain synthetic benchmarks, our DAL framework consistently achieved superior\nperformance across scenarios, indicating that the observed benefits are not an artifact of kernel\nchoice.\nBeyond direct comparisons, the broader motivation for adopting DKL lies in the challenge\nof kernel specification in our application domain. Each kernel encodes specific assumptions\nabout the underlying functional landscape—for example, RBF assumes infinitely differentiable\nsmoothness, while Matern allows controlled roughness. However, in electrolyte optimization\nthe true correlation structure among solvents, salts, and additives is highly complex and not\nknown a priori. Selecting and tuning a fixed kernel, or combining multiple kernels, requires\nstrong manual assumptions and extensive heuristic effort, which risks mis-specifying the model.\nBy contrast, DKL provides an adaptive mechanism to learn effective kernel representations\ndirectly from data, enabling the model to flexibly capture the relationships among solvents,\nsalts, and additives without relying on predetermined smoothness assumptions. This adaptivity\nis particularly valuable given the high experimental variability and the complex interactions\namong electrolyte formulations in our system.\nTo improve the justification, the text below has been inserted into the “Deep active\nlearning approach” Section of the revised manuscript: “On one hand, the deep neural network\ncan learn structure-property relationships directly from data, automatically forming adaptive\nkernel representations and thereby avoiding the need for manually defined covariance kernels\nwith predefined smoothness assumptions, which enhances the representation ability of models.”\n6. Along the same lines, the authors mention that “…the black-box functions with rapid\noscillations, which are characteristic of the objective function in the electrolyte optimization\nproblem…” But it has not been explicitly shown that the objective function for electrolyte\noptimization problem is indeed “rapidly oscillating”.\nOur response: By “rapid oscillations,” we refer to the large parameter–performance\ndiscontinuities observed in our experimental data. As shown in Supplementary Fig. 2 (here\ncited as Fig. R5 for readability), even when varying only one component (e.g., additive, lithium\nsalt concentration, salt identity, or solvent), the resulting cycle life shows sharp and non-\nmonotonic changes, rather than smooth trends. For instance, in Supplementary Figs. 2b, h,\nand k, small changes in composition can lead to either significant improvement or drastic\ndeterioration in lifetime, with no gradual transition. This confirms that the objective function in\nelectrolyte optimization is indeed highly non-smooth and discontinuous. To improve clarity ,\nwe have revised the manuscript to explicitly connect the term “rapid oscillations” with the\nexperimental evidence presented in Supplementary Fig. 2.\nAs illustrated in Supplementary Fig. 2, the space of electrolyte formulas is discrete in the\ndimensions of Li salts, solvents and additives, but somewhat relatively continuous in salt\nconcentrations (Supplementary Figs. 2d-f), which points to an objective function featuring\nboth discontinuous transitions and continuous variations. This sharp and non-monotonic\nresponse of cycle life to single-component changes demonstrates the “rapid oscillations” in the\nobjective function that characterize the electrolyte optimization problem. Therefore, a\nnumerical function of 𝑓 =(1−|𝑥|)sin(20(1−|𝑥|)6) was set up to simulate the process to\nverify the efficacy of the DAL approach based on the surrogate model of DKL (Fig. 2e and\ndetailed in Methods).\n7. The authors also make claims about DAL framework being able to balance between exploration and exploitation. This\ncan be explicitly shown on a reduced latent space representation of electrolytes from the trained DKL model by showing\nsuggestions from different batches. If the model is indeed exploiting, then the suggestions from later batches should\nconverge to a particular region of the chemical space. The authors can also show distribution of uncertainties for\nsuggestions from different batches and if the model is progressing towards exploitation, then the distribution of uncertainties\nshould shift towards lower values.\nOur response: Thank you for your comment. In fact, the dynamics of balancing exploration and\nexploitation during the DAL optimization are already reflected in Supplementary Fig. 5 (here\ncited as Fig. R6 for readability). Specifically:\nFirst, iteration improvement (Fig. R6a and b): The cycle life of the tested electrolytes\nshows consistent enhancement across iterations, with progressively diminishing gains (Fig.\nS6b). This trend demonstrates that the model initially explores a broader parameter space but\ngradually shifts towards exploitation by converging to high-performing regions.\nSecond, exploration-exploitation balance (Fig. R6c): The overlap of the suggested\ncandidates between the third and fourth iterations (orange points in the red box) highlights\nexploitation, as the model repeatedly focuses on promising regions. Meanwhile, the blue points\nwith relatively high uncertainty illustrate the continuing element of exploration, maintaining\ndiversity in the search.\nTogether, these results confirm that the DAL framework naturally achieves a balance\nbetween exploration and exploitation, consistent with the reviewer’s expectation.\n8. How are the molecular components represented? I do not see any discussion in the Methods section. Do they represent molecules using Morgan fingerprints or RDKit features or graph neural networks (GNN) or some sort of one-hot encoding? If one-hot encoding is used to represent molecular components in the electrolytes, then their model cannot really be inferred on molecular components unseen by the DKL model. If that’s the case, then the claim of “optimization over discrete electrolyte space” again does not really hold true.\nOur response: We thank the reviewer for raising this point. Representation of molecular\ncomponents is indeed central to our framework. We acknowledge that molecular fingerprints\n(e.g., Morgan), RDKit features, and graph neural networks (GNNs) are powerful tools for\ncheminformatics, as they encode detailed structural and physicochemical information. However,\nthese approaches are fundamentally designed for large-scale datasets. They rely on thousands\nor even millions of labeled molecules to learn stable representations and to generalize robustly\nto unseen structures. In contrast, electrolyte discovery operates under radically different\nconditions: each data point requires weeks to months of electrochemical testing, experimental\nreproducibility is limited, and datasets are inevitably small, sparse, and noisy. These constraints\nmake the aforementioned complex representations impractical, leading to inaccurate models\nand a high risk of overfitting. . Our approach therefore emphasizes a representation strategy\nthat is both experimentally feasible and aligned with the discrete, high-cost nature of electrolyte\noptimization. Specifically:\n(1) Representation strategy. In practice, we do not rely on simple one-hot encoding, which\nwould restrict the model to a closed set of molecules and prevent generalization. Instead, each\nelectrolyte formulation is represented by relational features that capture pairwise, triplet, and\nhigher-order interactions among salts, solvents, additives, and concentrations. These features\nare quantified using the average degree of interaction (ADI), defined as the mean cycle life\nacross all tested formulations containing a given component combination. For example, the\nADI between DOL and EC reflects the average cycle life measured across all electrolytes that\ninclude both solvents. This representation embeds experimentally derived interaction\nknowledge into the feature space and can be incrementally refined as additional data or new\ncomponents are incorporated. Such adaptability is integral to our two-stage framework, in\nwhich knowledge obtained from smaller, well-characterized spaces is systematically\ntransferred to larger or newly expanded spaces, thereby ensuring both scalability and continuity\nof optimization under realistic experimental conditions.\n(2) Why not molecular fingerprints or GNNs. These molecular representations are\nindeed powerful tools in cheminformatics, as they encode detailed structural and\nphysicochemical information and can, in principle, generalize to unseen molecules. However,\ntheir effectiveness relies on access to large, diverse, and well-labeled datasets. In electrolyte\ndiscovery, each new data point requires costly preparation and long-term cycling tests (often\nextending over weeks or months) making the collection of datasets at the scale required for\ngraph- or fingerprint-based approaches impractical. Our study instead targets discrete\nelectrolyte formulations, where the dominant challenge is to extract meaningful knowledge\nfrom scarce but high-value data. Relational features derived directly from experimental\noutcomes provide a more practical and chemically aligned representation, as they capture\ntransferable interaction knowledge that can be reused when the search space expands. This\nallows subsequent optimization to fully leverage prior insights rather than restarting from\nscratch, thereby improving efficiency under realistic experimental constraints.\n(3) Handling unseen components. We agree with the reviewer that predicting performance\nfor entirely new molecules is inherently challenging. Our framework is not intended for zero-\ndata prediction of unseen components, but rather supports few-shot transfer. When a new\nsolvent, salt, or additive is introduced, a limited number of targeted experiments are conducted\nto estimate its pairwise ADI values with existing components. Once these priors are established,\nthe model can incorporate the new component into the optimization process while leveraging\nthe interaction knowledge already captured from the existing component library. Importantly,\nthis adaptive mechanism allows the framework to expand iteratively over time,\nincorporating new molecules and enlarging the search space without the need for\ncomplete retraining.\n9. I also have reservations about their developed TSC approach. The average degree of interaction (ADI) values from this TSC approach can only be obtained post training of the DKL model and is not learned during the training itself. This limits the utility of this approach. Also, continuing from previous point, one needs to know the ADI values of unseen molecules a priori in order to make predictions: “For TSC coding the initial ADIs of DEP-or TO-related interactions were assigned as the prior 𝑝, which corresponds to the mean values of existing interactions.” This will severely limit the applicability of their approach on finding electrolytes constituting unexplored solvent, salts, or additives, as one would need to first perform real-world experiments using these unexplored molecular components.\nOur response: We thank the reviewer for this important comment. The reviewer is correct that\nthe Average Degree of Interaction (ADI) values are calculated post-training. ADI is not intended\nto be a predictive feature learned by the model itself, but rather a post-hoc abstraction of the\nknowledge captured by the trained DKL surrogate. It serves to distill the complex, non-linear\ncomponent interactions into an interpretable and transferable format.\nThe core of the reviewer’s concern is how to handle entirely new molecules. Our\nframework is designed for efficient few-shot optimization, not for zero-shot prediction, which\nremains a largely unsolved problem in experimental chemistry. When introducing a novel\ncomponent, we initialize its interaction values with the mean ADI of existing components. This\napproach provides an informed, neutral prior—a more principled starting point than a random\nguess—from which the active learning loop can begin.\nThe key is that this initial prior is not the final word; it is the starting point for exploration.\nThe framework is designed to leverage this prior to select the most informative initial\nexperiments involving the new molecule, allowing it to learn that molecule’s specific\ninteraction profile with maximum efficiency. This stands in sharp contrast to conventional\nmethods, which would require restarting the optimization from scratch and discarding all\npreviously acquired knowledge.\nThe practical power of this strategy is demonstrated in our results. As shown in Fig. 5b,\nour framework successfully identified a high-performing formulation containing new\nmolecular components within a single iteration of active learning. This result validates that the\nTSC-based knowledge transfer, even when initiated with a simple prior, dramatically\naccelerates discovery in expanded chemical spaces.\nWe have inserted the below text into the “Generalization ability of DAL for optimizing\nfull cells” Section of the revised manuscript to clarify this point: “This demonstrates that our\nDAL framework can effectively transfer previously acquired knowledge to guide electrolyte\ndesign involving newly introduced molecular components. By initializing unknown\ninteractions with statistically derived priors and incorporating only a small number of\nexperimental measurements, the framework dynamically expands the searchable space,\nenabling efficient optimization as new molecules are discovered without restarting the process.”\n10. Other non-technical comments:\na) The introduction section is a bit too long. Even though there is no word limit in the Nature Communications journal, I think it contains redundant information and so can be easily reduced to two-thirds.\nOur response: Done as suggested. Please refer to the Introduction Section (changes are marked\nin red) of the revised manuscript for the details.\nb) Some of the sentences are also too long and are hard to follow, e.g.:\n“To complicate it further, unlike the optimization of nonchemical (particularly numerical) subjects of interest – the examples of which include battery fast-charging protocols, and physical properties of electrolyte (solubility and concentration, ionic conductivities and viscosity) that vary over a continuous space of numbers – the materials space for electrolyte design is highly discrete, because the component-performance relationship is highly sensitive to many equilibria and inequilibria processes existing in the cell environment, such as the interphasial chemistry and related properties, where the change of a single chemical or its concentration may trigger an exponential increase in potential component interactions, resulting in the combinatorial explosion of search space.”\nOur response: Thank you for pointing this out. We have revised this sentence, and conducted a\nthorough review of the full text and revised other similarly lengthy expressions accordingly.\n“To complicate it further, unlike the optimization of nonchemical (particularly numerical)\nsubjects of interest—for example, battery fast-charging protocols or tuning electrolyte\nproperties of solubility, conductivity, and viscosity—the materials space for electrolyte design\nis highly discrete. This is because the relationship between components and performance is\nextremely sensitive to many equilibria and inequilibria processes existing in the cell\nenvironment. As a result, even a single component change can introduce exponential shifts in\nchemical interactions, leading to a combinatorial explosion of the design space.”\nc) Some of the words used in the draft can be replaced with more suitable ones, e.g.,\n“recommendation” with “suggestion” since the word recommendation gives the idea that a\nrecommendation system is being utilized to get new suggestions in each batch, which is not the\nsame as an AL framework.\nOur response: Done as suggested. The changes have been highlighted in red in the revised\nversion.\nd) Add a separate “Discussion” section in the revised draft (which is allowed as per journal’s guidelines) clearly highlighting limitations of their approach as pointed out above.\nOur response: Thank you for your comment. A new “Discussion and outlook” section has been\ninserted into the revised manuscript to clearly highlight the limitations of the proposed approach\nas pointed out above, which is reproduced below for your convenience.\nDiscussion and outlook\nIn this work, the two-stage optimization framework is developed in response to\npractical challenges, such as the high experimental cost, limited data availability, and\ninevitable data noise in electrolyte research. As an experiment-driven framework,\nimproving the treatment and even prediction of data noise through the DKL model will\nbe an important yet often overlooked direction for making experimental data more\nreliable and informative. Looking forward, with the advancement of experimental\nautomation and the accumulation of broader databases, more sophisticated methods—\nsuch as molecular encoding, which requires richer datasets—can be further integrated\ninto our DAL optimization framework. Importantly, the discreteness of electrolyte\nformulations remains intrinsic; thus, with more comprehensive and large-scale\ndatabases, the development of adaptive algorithms and optimization frameworks will\nbecome feasible. In addition, the TSC-based knowledge transfer serves as a critical tool\nfor quantifying electrolyte formulation design. It provides a pathway to map electrolyte\nmolecular chemistry onto electrochemical performance, offering quantifiable and\ncomparable metrics that can benefit electrolyte chemistry and formulation research.\nReviewer #2 (Remarks on code availability):\nComments on code availability have been discussed in the overall comments to the authors.\nOur response: Thank you for your comment.\nThe author describes a deep active learning approach to discover new electrolytes for lithium\nmetal batteries. Overall, the work is well structured and clearly presented. I believe that the\nnovelty lies in the combination of deep learning and active learning. However, the author\nprimarily focuses on convincing readers of the importance of this technique for improving the\nefficiency of electrolyte screening for lithium metal batteries. The main conclusions of the work\nappear somewhat scattered. I suggest that the author highlight the key novelty of the study more\nexplicitly. I have some concerns for the author to consider, listed below:\nOur response: Thank you for your valuable comments that largely help improve the quality of\nour manuscript. As suggested, we have revised the manuscript to more clearly highlight the key\nnovelty and contributions of this work.\n1.The work illustrated in the paper is too specific, and I can imagine that the author spent\nsubstantial time completing the experiments. How, then, can the author convince us that this\nmethod truly reduces time costs?\nOur response: We thank the reviewer for this comment and appreciate the recognition of the\nexperimental effort involved. The experimental validation in this study consists of two stages:\nIn the first stage, we conducted three rounds of active learning iterations within an initial\nspace of 720 electrolyte compositions, with each round testing only 32 electrolyte formulations.\nThis setup was deliberately designed to reflect realistic laboratory constraints, where exhaustive\ntesting of the combinatorial design space is impractical.\nIn the second stage, we performed targeted experimental validations in extended chemical\nspaces, including zero-shot predictions, one-round optimization in full-cell configuration, and\nan iteration involving new molecule integration via the DAL-TSC framework.\nAlthough the overall experimental process took time due to the nature of battery testing\n(each round requiring ~3 months), our method was able to identify high-performance\nelectrolyte formulations using only ~4.4% of the experimental resources compared to\ntraditional grid-search approaches. This demonstrates the efficiency of our framework in\nsignificantly reducing the experimental workload. More importantly, substantial time was saved\nin the optimization phase once the discrete nature of electrolyte performance was identified and\nthe DAL framework was in place.\n24\n2.The performance of lithium metal batteries is important; however, it is still not sufficient to\nrepresent or transfer the overall performance to other devices. Thus, the experimental design is\ncritical. LMO is not a typical cathode for lithium metal batteries—why not use NCM cathodes\nfor validation?\nOur response: Thank you for pointing this out. We agree that the relationship quantified by the\ncurrent optimization for Li|LMO cells cannot be directly transferred to other cathodes, because\nthey have different chemical requirements. We did not mean to achieve this goal as it is\nfundamentally impossible to do this. Our goal is to develop a two-state DAL framework that\ncombines the algorithm and chemical experiments. We can transfer the framework to\noptimization of other systems but we just need to input different set of experiments.\nWe apologize for the confusion caused by our terminology. To clarify, in our full-cell\nvalidation experiments, we indeed used NCM811 (LiNi Co Mn O ), which is a widely\n0.8 0.1 0.1 2\nadopted layered metal oxide cathode for lithium metal battery studies due to its high energy\ndensity and practical relevance. In the manuscript, we referred to it as a “layered metal oxide”,\nwhich might have been misinterpreted as spinel-type LiMn O , a different cathode chemistry.\n2 4\nWe have revised the manuscript to clearly indicate the use of NCM811 to avoid confusion.\n3.The authors need to emphasize the importance and necessity of DKL and Thompson sampling\nby comparing them with the standard BO process.\nOur response: We thank the reviewer for this valuable comment. The use of deep kernel learning\n(DKL) and Thompson sampling (TS) in our framework is a methodological necessity dictated\nby the unique characteristics of electrolyte discovery in this work. Conventional BO methods—\nbased on smooth surrogate functions and sequential sampling—are often effective for\ncontinuous, well-behaved optimization landscapes. However, electrolyte design exhibits\nfundamentally different characteristics. As shown in Supplementary Fig. 2, even a small\nvariation in formulation (e.g., changing an additive, lithium salt concentration, or solvent) can\nlead to sharp, non-monotonic changes in cycle life, resulting in a highly discontinuous and\nmultimodal objective surface. These characteristics violate the smoothness assumptions\ninherent to standard Gaussian Process (GP) models.\nMoreover, our experimental platform that is a 32-channel battery cycler allows\nsimultaneous testing of multiple electrolyte formulations, making large-batch parallel\nexploration essential to accelerate the optimization process optimization under costly and time-\nintensive evaluations. Our adoption of DKL and TS is thus driven by both the need for an\nadaptive mechanism to learn effective kernel representations and efficient large-batch parallel\nexploration, as elaborated below.\nas the radial basis function (RBF), which encodes infinitely differentiable smoothness. This\nassumption becomes restrictive when modeling the discrete and compositionally nonlinear\nlandscape of electrolyte formulations. DKL mitigates this limitation by introducing a learnable\nkernel structure:\n𝑘 (𝒙,𝒙′|𝝎,𝜽) = 𝑘 (𝑔(𝒙|𝝎),𝑔(𝒙′|𝝎)|𝜽) (1)\nDKL base\nwhere 𝑘 (𝒙,𝒙′) denotes the base kernel function, 𝜽 is the hyperparameter of the base\nbase\nkernel, and 𝑔 is the nonlinear mapping learned by the deep neural network, which is\nparameterized by the weights 𝝎.\nBy maximizing the marginal likelihood of DKL, we learn all deep kernel hyperparameters,\nincluding the parameter 𝝎 of the deep neural network and the parameter 𝜽 of the base kernel.\nThe kernel function in (1) achieves adaptive learning from the data by leveraging the flexible\nrepresentational capabilities of deep neural networks while maintaining the robust uncertainty\nquantification inherent to Gaussian processes. This stands in contrast to standard GP methods\nthat use traditional kernels, which are constrained by predefined similarity metrics. We\ndemonstrate the superior effectiveness of our proposed DKL approach in Fig. 2D of the revised\nmanuscript, where it successfully captures the complex relationships in electrolyte optimization\nthat elude conventional kernels.\nThompson sampling (TS). Efficient parallel exploration is a critical requirement imposed\nby our experimental workflow. Each experimental round is costly and time-consuming, yet our\nplatform enables simultaneous testing of multiple electrolyte formulations. To fully leverage\nthis capability and accelerate the optimization process, we need to select a diverse and\npromising batch of candidates at each iteration rather than a single point.\nThompson Sampling is well-suited for this batch scenario. To generate a batch of 𝑘\ncandidates (in our case, 𝑘=32), we can simply draw 𝑘 independent function samples from the\nposterior of the Gaussian Process surrogate model. The location of the maximum of each\nsample is then chosen as a candidate for the batch. This procedure is computationally efficient\nand naturally promotes exploration and diversity within the batch [R1], as each sample\nrepresents a different plausible hypothesis of the true objective function. In contrast, extending\nthe commonly used acquisition functions in standard BO like Expected Improvement (EI) to\nthe batch setting is more complex. A naive approach of simply selecting the top 𝑘 points with\nthe highest EI values would result in a highly redundant batch, with points clustered around a\nsingle peak in the acquisition function. More sophisticated methods like q-Expected\nImprovement (q-EI) are required to properly account for the joint improvement over a batch,\nbut they come at a much higher computational cost and implementation complexity [R2]. Given\nour experimental constraint of performing 32 parallel evaluations, TS offers an elegant, scalable,\nand effective acquisition strategy for maximizing the efficiency of our discovery workflow.\n26\n[R1] Kandasamy, K. et al. Parallelised Bayesian optimisation via Thompson sampling.\nInternational Conference on Artificial Intelligence and Statistics. 133-142 (2018).\n[R2] Gelbart, M.A. Constrained Bayesian Optimization and Applications. Harvard University,\n2015.\nTo address this comment, the text below has been inserted into:\n⚫ the second paragraph of the “Deep active learning approach” Section of the revised\nmanuscript: “On one hand, the deep neural network can learn structure-property\nrelationships directly from data, automatically forming adaptive kernel representations and\nthereby avoiding the need for manually defined covariance kernels with predefined\nsmoothness assumptions, which enhances the representation ability of models.”\n⚫ the fourth paragraph of the “Deep active learning approach” Section of the revised\nmanuscript: “To fully leverage the experimental throughput of parallel evaluations, an\nacquisition function of Thompson Sampling (see Methods) is then constructed based on\nthe posterior distribution from the surrogate model of DKL. This strategy enables scalable\nbatch-parallel optimization and efficiently sample the parameter space of electrolyte\nformulas by balancing exploration (i.e., testing regions with high uncertainty) and\nexploitation (i.e., testing promising regions based on completed experiment results) 50”\n4.Overall, I think this work is highly interdisciplinary. Researchers from the battery field and\nthe machine learning field could easily become confused. Therefore, integrating the two\neffectively will be a major challenge for the authors to address in order to improve the work.\nOur response: We thank the reviewer for this suggestion. To ensure clarity for readers from both\nbattery and machine learning fields, we have revised the Abstract, Introduction, and Conclusion\nsections to better highlight the fundamental motivation, the key technical challenges, and our\ncorresponding strategies. For clarity and readability, these revisions are marked in red in the\nrevised manuscript.\nReviewer #3 (Remarks on code availability):\nThe explanation of the code is not very well incorporated. I think the code needs to be\ncommented better for broader audience.\nOur response: Thank you for your comment. In the revised version, we have further improved\nthe code documentation and explanation to make it more accessible for a broader audience. All\nsource codes have been uploaded to our public GitHub repository\n(https://github.com/XWang1999/Electrolyte_Optimization_Deep_Active_Learning), which\n27\nnow includes detailed comments, structured docstrings, and comprehensive documentation\nspecifying the Python library dependencies and step-by-step instructions for reproducing the\noptimization workflow. Specifically:\n• The main demonstration notebook (Electrolyte_Optimization_Demo_DAL.ipynb) has\nbeen enriched with additional explanations and comments for each active learning\niteration, providing an executable example of how the method operates in practice.\n• The Deep Kernel Learning (DKL) implementation is provided in the dknet folder,\nwhich details the construction and training of the hybrid neural network–Gaussian\nprocess surrogate. In addition, a numerical example implemented in\nDAL_numerical_demo.py illustrates the optimization process on a benchmark test\nfunction, offering a clear demonstration of how the DKL-based surrogate performs\niterative learning and guides the search toward optimal regions.\n• For optimization in expanded parameter spaces, the framework can be directly\nextended by modifying the Target Statistic Coding (TSC) module according to the\nannotations and explanations provided in the notebook. This procedure enables\nknowledge transfer between tasks and has been explicitly described in both the\nmanuscript and the released code, ensuring that the workflow can be readily adapted\nfor broader electrolyte design and related optimization scenarios.\nThese improvements enhance the explanation of the code ensuring that researchers from\ndifferent backgrounds can readily understand and apply the workflow.\nNCOMMS-25-60533A\nWe thank the reviewers for their valuable comments. In response, we have carefully addressed each\npoint and incorporated the suggested changes into the revised manuscript (major changes are\nhighlighted in red for clarity), as detailed below. Answers to the reviewers’ comments are presented\nin blue, and the corresponding revised portions of the manuscript are copied here and marked in red.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThe manuscript has been revised pretty well according to the 1st round review. All my concerns\nhave been well addressed and I believe this work can cause wide interests and broad impact.\nOur response: We thank the reviewer for the positive assessment and are grateful for the helpful\ncomments from the first round, which have significantly strengthened the manuscript.\nReviewer #2 (Remarks to the Author):\nThe authors have provided a detailed response to my comments in the first round of revision and\nmany of my comments have been satisfactorily addressed, including the release of codes and\ndatasets. However, some critical comments remain unaddressed. See below:\n1. Comment #2 in the first round on predicting aleatoric uncertainties has not been taken care of but\ncan be addressed. I recommend the authors to follow this reference for guidance: Zhong et al., Nat.\nCommun. 16, 4522 (2025). Predicting aleatoric uncertainties is critical for quantifying\nreproducibility in the experimental measurements.\nOur response: We thank the reviewer for emphasizing the importance of explicitly modeling\naleatoric uncertainty and for pointing us to the recent work by Zhong et al. (Nat. Commun. 16, 4522,\n2025). Disentangling aleatoric and epistemic uncertainties is valuable for assessing experimental\nreproducibility and robustness. From an algorithmic perspective, Zhong et al. decompose predictive\nuncertainty by sampling from the posterior distribution of network weights, defining the aleatoric\ncomponent as the expected predictive entropy under fixed model parameters and the epistemic\ncomponent as the residual uncertainty induced by variability across weight samples. In contrast, our\nframework employs a Gaussian process with deep kernel learning under a homoscedastic noise\nassumption, in which observation noise is treated as input-independent. As a result, while the model\nprovides well-calibrated predictive uncertainty that primarily reflects epistemic uncertainty arising\nfrom sparse sampling and limited coverage of the compositional design space, it does not explicitly\nparameterize input-dependent aleatoric uncertainty. Consequently, a formal decomposition of\npredictive uncertainty into aleatoric and epistemic components is not directly supported within the\ncurrent modeling formulation.\nImportantly, this modeling choice is aligned with the primary objective of our study and is also\nconsistent with the conclusions reported by Zhong et al. (Nat. Commun. 16, 4522, 2025). In the\nsmall-sample experimental regime considered here, uncertainty estimates are used to guide\nexploration-exploitation trade-offs under a limited experimental budget, where epistemic\nuncertainty dominates and relative uncertainty rankings are sufficient for identifying informative\n1\nregions of the search space. Consistent with the findings of Zhong et al., in early-stage active\nlearning with limited data, uncertainty decomposition provides limited practical benefit due to\nunstable epistemic estimates, and acquisition strategies based on overall predictive uncertainty are\nmore robust and data-efficient, even in the absence of an explicit aleatoric-epistemic separation.\nWe agree with the reviewer that extending the present framework to explicitly model input-\ndependent aleatoric uncertainty represents an important direction for future work. While the current\nDKL-GP formulation adopts a homoscedastic noise assumption, future work will consider\nheteroscedastic Gaussian process models to explicitly capture input-dependent experimental noise,\nthereby improving uncertainty decomposition and reproducibility-oriented analyses. We have now\nexplicitly acknowledged this limitation and the corresponding future research direction in the\nDiscussion section of the revised manuscript.\n2. Comparison of t-SNE plots of all electrolytes (suggested ones should be clearly highlighted) from\ndifferent batches in point #7 in the first round are important. The authors can refer to this reference\nfor guidance: Khalak et al., J. Chem. Theory Comput. 18, 6259-6270 (2022) (Figure 5).\nOur response: We thank the reviewer for this suggestion. Low-dimensional visualizations are\npowerful for illustrating how an algorithm explores a complex design space. In Khalak et al. (J.\nChem. Theory Comput. 18, 6259-6270 (2022)), t-SNE is applied to a molecular encoding space,\nwhere each molecule is represented by a high-dimensional descriptor vector. In that context, the\nhigh dimensionality arises primarily from the choice of molecular descriptors and encoding scheme,\nand t-SNE is well suited to reveal latent structure in this continuous, descriptor-based chemical\nspace.\nIn our work, however, the underlying design problem is fundamentally different. We do not\noptimize over individual molecular structures, but over electrolyte formulations, which are defined\nby a finite set of discrete components (salt, solvent, additive) and their concentrations. Here, the\nincrease in dimensionality is driven by the combinatorial diversity of component types and mixing\nratios, rather than by a continuous, high-dimensional molecular descriptor space. Encoding each\nformulation into a high-dimensional vector (e.g., via one-hot representations of component\nidentities) and then applying t-SNE would mainly reflect the arbitrary categorical encoding of the\nformulation space, rather than a physically meaningful notion of molecular similarity. As a result,\nthe apparent “clusters” in such a t-SNE map would largely be determined by how the categories are\nencoded, and would not necessarily provide additional mechanistic insight into the electrolyte\nbehavior.\nFor this reason, instead of using a t-SNE embedding of a formulation encoding, we adopted a\ncomponent-resolved visualization strategy that is more directly aligned with how electrolyte\nformulations are designed and interpreted. In the revised manuscript, we explicitly analyze how\nDAL reshapes the exploration of the design space by tracking the evolution of: salt identity (Fig.\n3c), solvent identity (Supplementary Fig. 6e), salt concentration (Supplementary Fig. 21a), and\nadditive identity (Supplementary Fig. 22a) across different DAL iterations.\nThese plots show, for example, that DAL persistently and selectively explores formulations\ncontaining LiTFSI and LiFSI, while deprioritizing LiDFOB-rich regions after the first iteration due\nto their high experimental uncertainty and limited performance gains. This component-wise view\nmakes it transparent which parts of the formulation space are being exploited and which are being\ndiscarded, and it directly reflects the way experimentalists reason about multi-component\n2\nelectrolytes.\nWe have clarified this rationale and strengthened the discussion in the main text. The\ncorresponding paragraph now reads: “We now further show the success of DAL from a microscopic\nscale. Figure 3c shows the evolution of the space that is grouped by the type of salts (as a\nrepresentative). The electrolyte formulas for the first round are randomly selected with two replicate\ntests (first column in Fig. 3c) to generate an initial dataset for DAL model building. Through only\none DAL iteration, some electrolytes (i.e., those containing LiTFSI and LiFSI) are identified as\n“potential candidates” (second column in Fig. 3c). Interestingly, the LiDFOB regions (red dot area,\nfirst column in Fig. 3c) were allocated with many resources for the first iteration, but much fewer\nafter that, which indicates the high experimental uncertainty in this zone that requires careful\nvalidation. By learning and exploiting structural information of the parameter space, DAL avoids\nevaluating electrolytes with low estimated cell cycle life and directs more resources to the high-\nperformance region. This is also confirmed by individually analyzing other components of the space\n(discussed in Supplementary Fig. 6).”\nWe hope that this formulation-centric and component-resolved visualization adequately\naddresses the reviewer’s request for a clear depiction of how DAL navigates and concentrates the\nexploration within the electrolyte design space.\n3. The authors’ reasons for not using any chemical representation in the present framework is not\njustified (point #8 in the first round). If data-scarcity was the issue then one can use a pretrained\nmodel to generate molecular features for solvents, salts, and additives and feed to the surrogate\nmodel. The current approach may not lead to any new molecular design of electrolytes in a zero-\nshot manner, which stands in contrast to their claims of “optimization over discrete electrolyte\nspace”.\nOur response: We thank the reviewer for this point and for highlighting the possibility of using\npretrained molecular representations. The molecular foundation models are becoming central to de\nnovo molecular design, and pretrained encoders can provide rich molecular features for solvents,\nsalts, and additives.\nOur goal in this work, however, is more modest and differs in scope from de novo, zero-shot\nmolecular design. We focus on data-efficient optimization of electrolyte formulations for long-\nterm cycle life within a fixed, experimentally accessible library of salts, solvents, and additives,\nunder a specific cycling protocol. Each labeled data point corresponds to a full-cell life test that\ntypically requires months to complete and is strongly influenced by electrodes, cell geometry,\nformation procedures, and test conditions. Consequently, the number of reliably labeled\nformulations in our study is orders of magnitude smaller than the 104–106 molecules or mixtures\ntypically used to train or fine-tune current chemical foundation models, which are often built on\nMD-derived structural descriptors, transport properties, or equilibrium thermodynamic quantities.\nIn principle, one could take an existing pretrained molecular encoder and use it to generate\nfixed embeddings for the solvents, salts, and additives in our library, and then feed these embeddings\ninto the DKL surrogate model. In our setting, however, the main challenge is not only data scarcity,\nbut also task and domain misalignment between available pretrained models and our target\nproperty. Existing electrolyte-related foundation models are generally pretrained on simulated or\nliterature-derived data that emphasize equilibrium or short-timescale properties (e.g., solvation\nstructure, ionic conductivity, viscosity, density). By contrast, the cycle life of a full cell over\nhundreds of cycles is governed by long-timescale interfacial degradation, parasitic reactions, gas\nevolution, and coupled electrode-electrolyte failure mechanisms, which are only indirectly reflected\nin those pretraining tasks. In a small-data regime such as ours, adding high-dimensional molecular\nembeddings that are not well aligned with the target property can in fact make the surrogate harder\nto train and less stable, without guaranteeing a corresponding gain in predictive power.\nImportantly, our current framework does not omit chemical information; rather, it adopts a\nformulation-centric chemical representation that is tightly coupled to the experimental objective.\nInstead of representing individual molecules in a continuous descriptor space, we encode\nexperimentally derived interaction descriptors such as the ADI for pairs and higher-order\ncombinations of components. These features summarize, in a low-dimensional and task-specific\nway, how particular combinations of salts, solvents, and additives affect the observed cycle life\nacross all available formulations. As new experiments are performed, these interaction descriptors\nare updated, providing an end-to-end, experiment-driven representation that directly reflects the\n“composition-structure-performance” relationship relevant to long-term cycling stability.\nThis design has two practical consequences. First, it enables combinatorial optimization over\na large discrete formulation space spanned by a fixed library of experimentally accessible\ncomponents, which is the actual focus of this work. Second, it naturally supports few-shot expansion\nof the space: when a new component is introduced, only a small number of targeted experiments are\nneeded to estimate its interaction descriptors with existing components, after which it can be\nseamlessly integrated into the optimization loop without retraining a separate molecular encoder.\nTo avoid overstating our current capabilities, we have revised the wording of our claims in the\nAbstract and Discussion. Specifically, we replace “optimization over discrete electrolyte space”\nwith “optimization of formulations within a fixed discrete component library”. We also add a short\nparagraph in the Discussion outlining how pretrained molecular representation models could be\nintegrated into our framework in future work, once sufficiently large and task-aligned pretraining\ndatasets for long-term cycling performance become available.\n4. When I asked to include a “Discussion” section, the goal was for the authors to clearly highlight\nthe limitations. Currently, it is very brief and looks very generic and none of the main issues of their\napproach, which they themselves accept in responses to points #2, #8, and #9 from the first round,\nhave been explicitly highlighted in the manuscript. It is important to highlight all the limitations of\ntheir approach such that the reader is better informed and future.\nOur response: We thank the reviewer for this comment. Following the suggestions in both the first\nand second rounds, we have substantially revised the Discussion and outlook section to explicitly\nhighlight the main limitations of our framework, especially those related to points #2, #8, and #9.\nSpecifically, we now:\n1. Clarify the scope of optimization and the lack of zero-shot molecular design (related\nto points #8 and #9). We explicitly state that the current framework optimizes over\ncombinatorial electrolyte formulations built from a fixed, experimentally accessible\ncomponent library, and does not perform de novo, zero-shot molecular design. New\nsolvents, salts, or additives still require targeted experiments before they can be\nincorporated into the optimization.\n2. Highlight the limitations of our formulation-centric representation and the TSC/ADI\nscheme (related to points #8 and #9). We emphasize that chemical information is encoded\nvia interaction statistics (e.g., ADIs) rather than detailed molecule-level embeddings, and\nthat TSC and ADI are post-hoc abstractions. This design is pragmatic for small, noisy\ndatasets but limits our ability to capture fine-grained structure–property relationships and\nimplies a few-shot, rather than true zero-shot, capability for new components.\n3. Explicitly acknowledge limitations in uncertainty modeling (related to point #2). We\nclarify that the current framework models uncertainty under a homoscedastic noise\nassumption, and therefore does not explicitly disentangle or quantify input-dependent\naleatoric uncertainty. While this choice is appropriate for small-sample active learning\nwhere epistemic uncertainty dominates, extending the framework to heteroscedastic\nuncertainty modeling is considered as an important direction for future work and is now\nexplicitly discussed.\nThese revisions are now summarized in the Discussion and outlook section of the revised\nmanuscript: “In this work, we show that a DAL framework, built around a DKL surrogate and\nexperimentally derived interaction descriptors, can accelerate the discovery of long-lifespan\nelectrolyte formulations by steering experiments toward promising regions of a combinatorial\nformulation space. This implementation, however, is currently restricted to a fixed, experimentally\naccessible component library and to the specific cell chemistry and cycling protocol studied here; it\ndoes not perform de novo, zero-shot molecular design, but instead enables data-efficient\noptimization and few-shot expansion, for which newly introduced components still require targeted\nexperiments. Chemical information is encoded in a formulation-centric manner through interaction\nstatistics (such as ADIs), and TSC/ADI act as post hoc abstractions rather than learned molecular\nembeddings, which is pragmatic for small, noisy datasets but limits the resolution of structure-\nproperty relationships and generalization across chemically distant components. In addition, the\ncurrent framework models predictive uncertainty under a homoscedastic noise assumption, such\nthat uncertainty estimates primarily reflect epistemic uncertainty arising from sparse sampling and\nlimited coverage of the formulation space. As a result, input-dependent aleatoric uncertainty is not\nexplicitly quantified, which constrains the assessment of experimental variability and\nreproducibility across heterogeneous conditions. Looking ahead, as larger, task-aligned electrolyte\ndatasets available, molecular foundation models and pretrained mixture-level encoders could be\nintegrated with these interaction-based features to improve generalization, while heteroscedastic\nuncertainty modeling could further enhance the characterization of experimental variability and\nreproducibility, all while preserving data efficiency and enabling a gradual transition from\nformulation-level optimization toward more genuine molecular design.\nReviewer #3 (Remarks to the Author):\nI appreciate the response of the authors to my comments. I think the questions are overall very well\npresented. However, the answer to my Comment #4 is vague. I cannot find the details about the\nimprovements completed by the author. The improvements to enhanced the significant of this work\nto the audience is highly essential. I hope this point can be addressed further.\nOur response: We thank the reviewer for the follow-up comment, and we apologize that our previous\nresponse did not clearly describe the corresponding revisions. In the revised manuscript, we have\nimplemented several concrete changes to make the interdisciplinary significance of this work more\nexplicit for both battery and machine-learning audiences:\n1. Abstract (last two sentences). We have rewritten the final two sentences of the Abstract\nto clearly state what the framework offers to each community. This change is intended to\nexplicitly communicate the relevance of our framework to both readerships at the very\nbeginning of the paper. The Abstract now ends with: “This work provides an experiment-\ndriven, sample-efficient route to explore complex electrolyte formulation spaces and\nquantify inter-component correlations, as well as a realistic, high-cost, small-data\nbenchmark for probabilistic surrogate modeling and sequential decision-making in discrete\nchemical spaces. Together, these advances establish an AI-assisted discovery framework\nfor rapid exploration, knowledge learning and transfer in complex materials spaces, without\nrelying on detailed mechanistic models or empirical design rules.”\n2. Introduction (new “bridge” sentence). At the end of the Introduction, we have added an\nexplicit bridging sentence that summarizes what each community can take away from the\nDAL–TSC workflow:\n“From the perspective of battery research, this framework organizes costly cycling\nexperiments into a structured, sample-efficient exploration of electrolyte formulations;\nfrom the perspective of machine learning, it provides a realistic, high-cost and small-data\ntestbed for probabilistic surrogate modeling and sequential decision-making in discrete\nchemical spaces.”\nThis sentence is meant to guide battery researchers in understanding how the method\ntranslates into practical experimental strategies, and to help machine-learning researchers\nview the work as a well-defined benchmark problem rather than a black-box application.\n3. Discussion and outlook (explicit limitations and future directions). We have\nsubstantially revised the Discussion and outlook section to make the limitations and future\nneeds of this cross-disciplinary approach explicit for both fields. In particular, we now\nemphasize that:\n(i) the present DAL–DKL implementation is restricted to a fixed, experimentally accessible\ncomponent library and a specific cell chemistry and protocol, and thus does not perform de\nnovo, zero-shot molecular design;\n(ii) chemical information is encoded in a formulation-centric manner through interaction\nstatistics (such as ADIs), with TSC/ADI acting as post-hoc abstractions rather than learned\nmolecular embeddings, which is pragmatic for small, noisy datasets but limits structure–\nproperty resolution and generalization across chemically distant components; and\n(iii) the workflow still relies on specific design choices (component library, network\narchitecture, acquisition strategy and noise treatment) that may require adaptation in other\nchemistries or testing protocols.\nWe also explicitly outline future research directions on both sides: the need for larger, task-\naligned electrolyte datasets and more physically grounded electrolyte models from the\nbattery perspective, and the opportunity to integrate molecular foundation models and\npretrained mixture-level encoders with our interaction-based features from the machine-\nlearning perspective, in order to move from formulation-level optimization toward more\ngenuine molecular design.\nWe hope that these targeted revisions clarify both the significance and the current limitations\nof our interdisciplinary framework for readers from the battery and machine-learning communities."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript has been revised pretty well according to the 1st round review. All my concerns have been well addressed and I believe this work can cause wide interests and broad impact.", "reviewer_2": "The authors have provided a detailed response to my comments in the first round of revision and many of my comments have been satisfactorily addressed, including the release of codes and datasets. However, some critical comments remain unaddressed. See below:\n1. Comment #2 in the first round on predicting aleatoric uncertainties has not been taken care of but can be addressed. I recommend the authors to follow this reference for guidance: Zhong et al., Nat. Commun. 16, 4522 (2025). Predicting aleatoric uncertainties is critical for quantifying reproducibility in the experimental measurements.\n2. Comparison of t-SNE plots of all electrolytes (suggested ones should be clearly highlighted) from different batches in point #7 in the first round are important. The authors can refer to this reference for guidance: Khalak et al., J. Chem. Theory Comput. 18, 6259-6270 (2022) (Figure 5).\n3. The authors’ reasons for not using any chemical representation in the present framework is not justified (point #8 in the first round). If data-scarcity was the issue then one can use a pretrained model to generate molecular features for solvents, salts, and additives and feed to the surrogate model. The current approach may not lead to any new molecular design of electrolytes in a zero-shot manner, which stands in contrast to their claims of “optimization over discrete electrolyte space”.\n4. When I asked to include a “Discussion” section, the goal was for the authors to clearly highlight the limitations. Currently, it is very brief and looks very generic and none of the main issues of their approach, which they themselves accept in responses to points #2, #8, and #9 from the first round, have been explicitly highlighted in the manuscript. It is important to highlight all the limitations of their approach such that the reader is better informed and future.", "reviewer_3": "I appreciate the response of the authors to my comments. I think the questions are overall very well presented. However, the answer to my Comment #4 is vague. I cannot find the details about the improvements completed by the author. The improvements to enhanced the significant of this work to the audience is highly essential. I hope this point can be addressed further."}, "author_response": "Response Letter to Reviewers’ Comments on Manuscript\nNCOMMS-25-60533A\nWe thank the reviewers for their valuable comments. In response, we have carefully addressed each\npoint and incorporated the suggested changes into the revised manuscript (major changes are\nhighlighted in red for clarity), as detailed below. Answers to the reviewers’ comments are presented\nin blue, and the corresponding revised portions of the manuscript are copied here and marked in red.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThe manuscript has been revised pretty well according to the 1st round review. All my concerns\nhave been well addressed and I believe this work can cause wide interests and broad impact.\nOur response: We thank the reviewer for the positive assessment and are grateful for the helpful\ncomments from the first round, which have significantly strengthened the manuscript.\nReviewer #2 (Remarks to the Author):\nThe authors have provided a detailed response to my comments in the first round of revision and\nmany of my comments have been satisfactorily addressed, including the release of codes and\ndatasets. However, some critical comments remain unaddressed. See below:\n1. Comment #2 in the first round on predicting aleatoric uncertainties has not been taken care of but\ncan be addressed. I recommend the authors to follow this reference for guidance: Zhong et al., Nat.\nCommun. 16, 4522 (2025). Predicting aleatoric uncertainties is critical for quantifying\nreproducibility in the experimental measurements.\nOur response: We thank the reviewer for emphasizing the importance of explicitly modeling\naleatoric uncertainty and for pointing us to the recent work by Zhong et al. (Nat. Commun. 16, 4522,\n2025). Disentangling aleatoric and epistemic uncertainties is valuable for assessing experimental\nreproducibility and robustness. From an algorithmic perspective, Zhong et al. decompose predictive\nuncertainty by sampling from the posterior distribution of network weights, defining the aleatoric\ncomponent as the expected predictive entropy under fixed model parameters and the epistemic\ncomponent as the residual uncertainty induced by variability across weight samples. In contrast, our\nframework employs a Gaussian process with deep kernel learning under a homoscedastic noise\nassumption, in which observation noise is treated as input-independent. As a result, while the model\nprovides well-calibrated predictive uncertainty that primarily reflects epistemic uncertainty arising\nfrom sparse sampling and limited coverage of the compositional design space, it does not explicitly\nparameterize input-dependent aleatoric uncertainty. Consequently, a formal decomposition of\npredictive uncertainty into aleatoric and epistemic components is not directly supported within the\ncurrent modeling formulation.\nImportantly, this modeling choice is aligned with the primary objective of our study and is also\nconsistent with the conclusions reported by Zhong et al. (Nat. Commun. 16, 4522, 2025). In the\nsmall-sample experimental regime considered here, uncertainty estimates are used to guide\nexploration-exploitation trade-offs under a limited experimental budget, where epistemic\nuncertainty dominates and relative uncertainty rankings are sufficient for identifying informative\n1\nregions of the search space. Consistent with the findings of Zhong et al., in early-stage active\nlearning with limited data, uncertainty decomposition provides limited practical benefit due to\nunstable epistemic estimates, and acquisition strategies based on overall predictive uncertainty are\nmore robust and data-efficient, even in the absence of an explicit aleatoric-epistemic separation.\nWe agree with the reviewer that extending the present framework to explicitly model input-\ndependent aleatoric uncertainty represents an important direction for future work. While the current\nDKL-GP formulation adopts a homoscedastic noise assumption, future work will consider\nheteroscedastic Gaussian process models to explicitly capture input-dependent experimental noise,\nthereby improving uncertainty decomposition and reproducibility-oriented analyses. We have now\nexplicitly acknowledged this limitation and the corresponding future research direction in the\nDiscussion section of the revised manuscript.\n2. Comparison of t-SNE plots of all electrolytes (suggested ones should be clearly highlighted) from\ndifferent batches in point #7 in the first round are important. The authors can refer to this reference\nfor guidance: Khalak et al., J. Chem. Theory Comput. 18, 6259-6270 (2022) (Figure 5).\nOur response: We thank the reviewer for this suggestion. Low-dimensional visualizations are\npowerful for illustrating how an algorithm explores a complex design space. In Khalak et al. (J.\nChem. Theory Comput. 18, 6259-6270 (2022)), t-SNE is applied to a molecular encoding space,\nwhere each molecule is represented by a high-dimensional descriptor vector. In that context, the\nhigh dimensionality arises primarily from the choice of molecular descriptors and encoding scheme,\nand t-SNE is well suited to reveal latent structure in this continuous, descriptor-based chemical\nspace.\nIn our work, however, the underlying design problem is fundamentally different. We do not\noptimize over individual molecular structures, but over electrolyte formulations, which are defined\nby a finite set of discrete components (salt, solvent, additive) and their concentrations. Here, the\nincrease in dimensionality is driven by the combinatorial diversity of component types and mixing\nratios, rather than by a continuous, high-dimensional molecular descriptor space. Encoding each\nformulation into a high-dimensional vector (e.g., via one-hot representations of component\nidentities) and then applying t-SNE would mainly reflect the arbitrary categorical encoding of the\nformulation space, rather than a physically meaningful notion of molecular similarity. As a result,\nthe apparent “clusters” in such a t-SNE map would largely be determined by how the categories are\nencoded, and would not necessarily provide additional mechanistic insight into the electrolyte\nbehavior.\nFor this reason, instead of using a t-SNE embedding of a formulation encoding, we adopted a\ncomponent-resolved visualization strategy that is more directly aligned with how electrolyte\nformulations are designed and interpreted. In the revised manuscript, we explicitly analyze how\nDAL reshapes the exploration of the design space by tracking the evolution of: salt identity (Fig.\n3c), solvent identity (Supplementary Fig. 6e), salt concentration (Supplementary Fig. 21a), and\nadditive identity (Supplementary Fig. 22a) across different DAL iterations.\nThese plots show, for example, that DAL persistently and selectively explores formulations\ncontaining LiTFSI and LiFSI, while deprioritizing LiDFOB-rich regions after the first iteration due\nto their high experimental uncertainty and limited performance gains. This component-wise view\nmakes it transparent which parts of the formulation space are being exploited and which are being\ndiscarded, and it directly reflects the way experimentalists reason about multi-component\n2\nelectrolytes.\nWe have clarified this rationale and strengthened the discussion in the main text. The\ncorresponding paragraph now reads: “We now further show the success of DAL from a microscopic\nscale. Figure 3c shows the evolution of the space that is grouped by the type of salts (as a\nrepresentative). The electrolyte formulas for the first round are randomly selected with two replicate\ntests (first column in Fig. 3c) to generate an initial dataset for DAL model building. Through only\none DAL iteration, some electrolytes (i.e., those containing LiTFSI and LiFSI) are identified as\n“potential candidates” (second column in Fig. 3c). Interestingly, the LiDFOB regions (red dot area,\nfirst column in Fig. 3c) were allocated with many resources for the first iteration, but much fewer\nafter that, which indicates the high experimental uncertainty in this zone that requires careful\nvalidation. By learning and exploiting structural information of the parameter space, DAL avoids\nevaluating electrolytes with low estimated cell cycle life and directs more resources to the high-\nperformance region. This is also confirmed by individually analyzing other components of the space\n(discussed in Supplementary Fig. 6).”\nWe hope that this formulation-centric and component-resolved visualization adequately\naddresses the reviewer’s request for a clear depiction of how DAL navigates and concentrates the\nexploration within the electrolyte design space.\n3. The authors’ reasons for not using any chemical representation in the present framework is not\njustified (point #8 in the first round). If data-scarcity was the issue then one can use a pretrained\nmodel to generate molecular features for solvents, salts, and additives and feed to the surrogate\nmodel. The current approach may not lead to any new molecular design of electrolytes in a zero-\nshot manner, which stands in contrast to their claims of “optimization over discrete electrolyte\nspace”.\nOur response: We thank the reviewer for this point and for highlighting the possibility of using\npretrained molecular representations. The molecular foundation models are becoming central to de\nnovo molecular design, and pretrained encoders can provide rich molecular features for solvents,\nsalts, and additives.\nOur goal in this work, however, is more modest and differs in scope from de novo, zero-shot\nmolecular design. We focus on data-efficient optimization of electrolyte formulations for long-\nterm cycle life within a fixed, experimentally accessible library of salts, solvents, and additives,\nunder a specific cycling protocol. Each labeled data point corresponds to a full-cell life test that\ntypically requires months to complete and is strongly influenced by electrodes, cell geometry,\nformation procedures, and test conditions. Consequently, the number of reliably labeled\nformulations in our study is orders of magnitude smaller than the 104–106 molecules or mixtures\ntypically used to train or fine-tune current chemical foundation models, which are often built on\nMD-derived structural descriptors, transport properties, or equilibrium thermodynamic quantities.\nIn principle, one could take an existing pretrained molecular encoder and use it to generate\nfixed embeddings for the solvents, salts, and additives in our library, and then feed these embeddings\ninto the DKL surrogate model. In our setting, however, the main challenge is not only data scarcity,\nbut also task and domain misalignment between available pretrained models and our target\nproperty. Existing electrolyte-related foundation models are generally pretrained on simulated or\nliterature-derived data that emphasize equilibrium or short-timescale properties (e.g., solvation\nstructure, ionic conductivity, viscosity, density). By contrast, the cycle life of a full cell over\nhundreds of cycles is governed by long-timescale interfacial degradation, parasitic reactions, gas\nevolution, and coupled electrode-electrolyte failure mechanisms, which are only indirectly reflected\nin those pretraining tasks. In a small-data regime such as ours, adding high-dimensional molecular\nembeddings that are not well aligned with the target property can in fact make the surrogate harder\nto train and less stable, without guaranteeing a corresponding gain in predictive power.\nImportantly, our current framework does not omit chemical information; rather, it adopts a\nformulation-centric chemical representation that is tightly coupled to the experimental objective.\nInstead of representing individual molecules in a continuous descriptor space, we encode\nexperimentally derived interaction descriptors such as the ADI for pairs and higher-order\ncombinations of components. These features summarize, in a low-dimensional and task-specific\nway, how particular combinations of salts, solvents, and additives affect the observed cycle life\nacross all available formulations. As new experiments are performed, these interaction descriptors\nare updated, providing an end-to-end, experiment-driven representation that directly reflects the\n“composition-structure-performance” relationship relevant to long-term cycling stability.\nThis design has two practical consequences. First, it enables combinatorial optimization over\na large discrete formulation space spanned by a fixed library of experimentally accessible\ncomponents, which is the actual focus of this work. Second, it naturally supports few-shot expansion\nof the space: when a new component is introduced, only a small number of targeted experiments are\nneeded to estimate its interaction descriptors with existing components, after which it can be\nseamlessly integrated into the optimization loop without retraining a separate molecular encoder.\nTo avoid overstating our current capabilities, we have revised the wording of our claims in the\nAbstract and Discussion. Specifically, we replace “optimization over discrete electrolyte space”\nwith “optimization of formulations within a fixed discrete component library”. We also add a short\nparagraph in the Discussion outlining how pretrained molecular representation models could be\nintegrated into our framework in future work, once sufficiently large and task-aligned pretraining\ndatasets for long-term cycling performance become available.\n4. When I asked to include a “Discussion” section, the goal was for the authors to clearly highlight\nthe limitations. Currently, it is very brief and looks very generic and none of the main issues of their\napproach, which they themselves accept in responses to points #2, #8, and #9 from the first round,\nhave been explicitly highlighted in the manuscript. It is important to highlight all the limitations of\ntheir approach such that the reader is better informed and future.\nOur response: We thank the reviewer for this comment. Following the suggestions in both the first\nand second rounds, we have substantially revised the Discussion and outlook section to explicitly\nhighlight the main limitations of our framework, especially those related to points #2, #8, and #9.\nSpecifically, we now:\n1. Clarify the scope of optimization and the lack of zero-shot molecular design (related\nto points #8 and #9). We explicitly state that the current framework optimizes over\ncombinatorial electrolyte formulations built from a fixed, experimentally accessible\ncomponent library, and does not perform de novo, zero-shot molecular design. New\nsolvents, salts, or additives still require targeted experiments before they can be\nincorporated into the optimization.\n2. Highlight the limitations of our formulation-centric representation and the TSC/ADI\nscheme (related to points #8 and #9). We emphasize that chemical information is encoded\nvia interaction statistics (e.g., ADIs) rather than detailed molecule-level embeddings, and\nthat TSC and ADI are post-hoc abstractions. This design is pragmatic for small, noisy\ndatasets but limits our ability to capture fine-grained structure–property relationships and\nimplies a few-shot, rather than true zero-shot, capability for new components.\n3. Explicitly acknowledge limitations in uncertainty modeling (related to point #2). We\nclarify that the current framework models uncertainty under a homoscedastic noise\nassumption, and therefore does not explicitly disentangle or quantify input-dependent\naleatoric uncertainty. While this choice is appropriate for small-sample active learning\nwhere epistemic uncertainty dominates, extending the framework to heteroscedastic\nuncertainty modeling is considered as an important direction for future work and is now\nexplicitly discussed.\nThese revisions are now summarized in the Discussion and outlook section of the revised\nmanuscript: “In this work, we show that a DAL framework, built around a DKL surrogate and\nexperimentally derived interaction descriptors, can accelerate the discovery of long-lifespan\nelectrolyte formulations by steering experiments toward promising regions of a combinatorial\nformulation space. This implementation, however, is currently restricted to a fixed, experimentally\naccessible component library and to the specific cell chemistry and cycling protocol studied here; it\ndoes not perform de novo, zero-shot molecular design, but instead enables data-efficient\noptimization and few-shot expansion, for which newly introduced components still require targeted\nexperiments. Chemical information is encoded in a formulation-centric manner through interaction\nstatistics (such as ADIs), and TSC/ADI act as post hoc abstractions rather than learned molecular\nembeddings, which is pragmatic for small, noisy datasets but limits the resolution of structure-\nproperty relationships and generalization across chemically distant components. In addition, the\ncurrent framework models predictive uncertainty under a homoscedastic noise assumption, such\nthat uncertainty estimates primarily reflect epistemic uncertainty arising from sparse sampling and\nlimited coverage of the formulation space. As a result, input-dependent aleatoric uncertainty is not\nexplicitly quantified, which constrains the assessment of experimental variability and\nreproducibility across heterogeneous conditions. Looking ahead, as larger, task-aligned electrolyte\ndatasets available, molecular foundation models and pretrained mixture-level encoders could be\nintegrated with these interaction-based features to improve generalization, while heteroscedastic\nuncertainty modeling could further enhance the characterization of experimental variability and\nreproducibility, all while preserving data efficiency and enabling a gradual transition from\nformulation-level optimization toward more genuine molecular design.\nReviewer #3 (Remarks to the Author):\nI appreciate the response of the authors to my comments. I think the questions are overall very well\npresented. However, the answer to my Comment #4 is vague. I cannot find the details about the\nimprovements completed by the author. The improvements to enhanced the significant of this work\nto the audience is highly essential. I hope this point can be addressed further.\nOur response: We thank the reviewer for the follow-up comment, and we apologize that our previous\nresponse did not clearly describe the corresponding revisions. In the revised manuscript, we have\nimplemented several concrete changes to make the interdisciplinary significance of this work more\nexplicit for both battery and machine-learning audiences:\n1. Abstract (last two sentences). We have rewritten the final two sentences of the Abstract\nto clearly state what the framework offers to each community. This change is intended to\nexplicitly communicate the relevance of our framework to both readerships at the very\nbeginning of the paper. The Abstract now ends with: “This work provides an experiment-\ndriven, sample-efficient route to explore complex electrolyte formulation spaces and\nquantify inter-component correlations, as well as a realistic, high-cost, small-data\nbenchmark for probabilistic surrogate modeling and sequential decision-making in discrete\nchemical spaces. Together, these advances establish an AI-assisted discovery framework\nfor rapid exploration, knowledge learning and transfer in complex materials spaces, without\nrelying on detailed mechanistic models or empirical design rules.”\n2. Introduction (new “bridge” sentence). At the end of the Introduction, we have added an\nexplicit bridging sentence that summarizes what each community can take away from the\nDAL–TSC workflow:\n“From the perspective of battery research, this framework organizes costly cycling\nexperiments into a structured, sample-efficient exploration of electrolyte formulations;\nfrom the perspective of machine learning, it provides a realistic, high-cost and small-data\ntestbed for probabilistic surrogate modeling and sequential decision-making in discrete\nchemical spaces.”\nThis sentence is meant to guide battery researchers in understanding how the method\ntranslates into practical experimental strategies, and to help machine-learning researchers\nview the work as a well-defined benchmark problem rather than a black-box application.\n3. Discussion and outlook (explicit limitations and future directions). We have\nsubstantially revised the Discussion and outlook section to make the limitations and future\nneeds of this cross-disciplinary approach explicit for both fields. In particular, we now\nemphasize that:\n(i) the present DAL–DKL implementation is restricted to a fixed, experimentally accessible\ncomponent library and a specific cell chemistry and protocol, and thus does not perform de\nnovo, zero-shot molecular design;\n(ii) chemical information is encoded in a formulation-centric manner through interaction\nstatistics (such as ADIs), with TSC/ADI acting as post-hoc abstractions rather than learned\nmolecular embeddings, which is pragmatic for small, noisy datasets but limits structure–\nproperty resolution and generalization across chemically distant components; and\n(iii) the workflow still relies on specific design choices (component library, network\narchitecture, acquisition strategy and noise treatment) that may require adaptation in other\nchemistries or testing protocols.\nWe also explicitly outline future research directions on both sides: the need for larger, task-\naligned electrolyte datasets and more physically grounded electrolyte models from the\nbattery perspective, and the opportunity to integrate molecular foundation models and\npretrained mixture-level encoders with our interaction-based features from the machine-\nlearning perspective, in order to move from formulation-level optimization toward more\ngenuine molecular design.\nWe hope that these targeted revisions clarify both the significance and the current limitations\nof our interdisciplinary framework for readers from the battery and machine-learning communities."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The comments have been addressed."}, "author_response": ""}]

Decision letter