Data-driven intelligent carbonization unifies diverse biomass into high-performance hard carbon negative electrodes

Domain: biology
Published: 2026-03-13
Editorial outcome: major_revision

Abstract
Sustainable batteries necessitate high-performance hard carbon negative electrodes derived from abundant biomass. However, realizing their full potential is significantly limited by the inherent diversity of biomass feedstocks, the intricate control over carbonization and resulting microstructures, and the complex interplay between processing, structure, and electrochemical performance. Here, we introduce “intelligent carbonization”, a strategy integrating programmable Joule heating (1000-2000 °C, 10-60 s) with machine learning to substantially accelerate the discovery and optimization of biomass-derived hard carbons. By mapping over 1000 synthetic pathways and decoding the multidimensional feature space, we reveal a performance-correlated factor that serves as a crucial predictor of capacity, complementing conventional graphitic descriptors (in-plane crystallite size/ interlayer spacing). By a minimal energy input (0.1 kWh g-1), our strategy converts biochar into advanced hard carbon delivering 369 mAh g-1 reversible capacity, high rate capability, and improved cycling stability (>5000 cycles at a specific current of 3 A g-1). This data-centric approach allows low-cost and intelligent manufacturing of diverse biomass resources into performance-unified hard carbon negative electrodes, thereby paving the way for practical and large-scale biomass valorization towards sustainable energy storage solutions.

Introduction
With an annual global production exceeding 220 billion oven dry tonne (odt) (or 4500EJ)1, biomass stands as an exceptionally vast, renewable, and ubiquitous reservoir, offering considerable potential for carbon-neutral product development2-5. The conversion of biomass into sustainable hard carbon (HC) negative electrodes is critical for fast charging lithium-ion batteries and particularly industrializing sodium-ion batteries (SIBs), which target large-scale grid storage demanding vast material supply and costs below $50 per kWh6. This dual role in energy storage and resource valorization underscores the importance of HC in advancing both renewable energy technologies and sustainable industrial practices. However, the complex and variable nature of biomass precursors makes it difficult to produce HC with consistent and predictable properties7-9, typically scattering from 150-300 mAh g-1, posing a significant barrier to industrial-scale manufacturing. Furthermore, the unpredictable nature of carbonization and the unclear structure-property relationship hinders the rational design of HC from diverse biomass resources. Addressing these fundamental challenges is key to unlocking the full potential of biomass in next-generation energy storage.

Conventionally, HCs are produced via a two-step carbonization: 1) a low-temperature pyrolysis (~700°C) to yield the biochar, and 2) a high-temperature carbonization10-15 (e.g., 1400–1500°C for >2 hours) to tailor the graphitic microstructure of biochar into HC. While the biochar is abundant and cheap, the simple pyrolysis leads to premature microstructures and unsatisfactory performance (<200 mAh g-1)16, 17 (Fig. 1a). The latter carbonization stage, crucial for forming HC, is notably energy-intensive and incurs significant carbon emissions. Importantly, after this prolonged carbonization, HCs possess a complex microstructure with randomly oriented graphitic microcrystals, amorphous regions, and nanopores18-20, leading to variations in microstructure and performance across different biomass sources. For example, the rigid, lignin-containing frameworks of wood21, 22 and bamboo23 tend to produce carbons with robust, hierarchical pore systems; In contrast, the highly crystalline and pure cellulose from cotton11 is more conducive to forming well-ordered graphitic domains, translating into differing electrochemical behaviors (134~300 mAh g-1)24, 25. Moreover, the convoluted evolution of multiple structural parameters—such as graphitic microcrystal size, interlayer spacing, and porosity—is inherent to conventional carbonization26-30, posing a profound challenge of elucidating their structure-performance relationships. Consequently, the development of HC has been largely confined to an empirical, trial-and-error paradigm. While targeted synthetic strategies have provided initial insights correlating structure with reversible capacity, a quantitative and predictive understanding remains elusive31. In sum, developing biomass-derived HCs is hindered by three major challenges: 1) the energy-intensive carbonization process; 2) biomass diversity and performance variations; and 3) complex process-structure-property correlations for understanding and rational design.

Accordingly, establishing a paradigm for efficient, predictable, and genuinely sustainable manufacturing of HC with consistent performance is critical to advancing SIB technology. Herein, by integrating energy-efficient programmable Joule heating32, 33 (PJH) with machine learning (ML), our intelligent carbonization strategy unveils a critical capacity descriptor that unlocks the sustainable production of consistent HC from diverse biomass (Fig. 1b). The centerpiece of our discovery is a performance-correlated factor (PCF), derived from X-ray diffraction (XRD) data, which critically supplements traditional metrics like La and d002, together enabling a predictive model with greater accuracy for electrochemical capacity. This allows us to yield digital HC (Dig-HC) that exhibits a capacity of 369 mAh g⁻¹ (at 0.2 C, 1 C=300 mA g-1), more than doubling the biochar’s capacity of 150 mAh g⁻¹ (Fig. 1c), while also showing strong rate performance (280 mAh g⁻¹ at 10 C) and >5000 cycle stability. Critically, this improvement is achieved by PJH synthesis in an exceptionally energy-efficient manner34, consuming merely 0.1 kWh g-1 of electrical energy (~6% compared to biochar production). Our approach enables the production of a sustainable and high-performing Dig-HC from low cost biochar with an estimated production cost of ~$6,000 per ton—less than reported HCs (Fig. 1d). Leveraging this strategy, we demonstrate a full life sustainability pathway for HC negative electrodes: from renewable biomass, through an energy-efficient electrified carbonization process, to a durable high-performance HC negative electrode that enables a more resilient and sustainable energy future.

Results
Synthesis and process optimization guided by machine learning.
While ML holds significant promise for materials science35-37, its application to HCs has been constrained by the bottleneck of slow, traditional experimental data acquisition. Specifically, while the initial synthesis of biochar from biomass via low temperature pyrolysis (T1: 600-800 °C, t1: 1-2 h) (Supplementary Fig. 1) is a rapid, high-throughput, and energetically favorable process, its conversion into HC is hampered by a lengthy and energy-intensive high-temperature carbonization (1400-1600 °C) that requires over 500 minutes. Our PJH carbonization strategy circumvents this limitation and completes the transformation from biochar to HC in under one minute (Fig. 2a, Supplementary Table 1). Compared to conventional carbonization, our method reduces the processing time by 500 times while requiring only 0.1 kWh g-1 of the energy input (Fig. 2b), with the detailed calculation shown in Supplementary Note 1. Despite the sub-minute processing time, XRD analysis confirmed that this rapid synthesis method does not sacrifice structural quality (Fig. 2c). The PJH treatment was sufficient to increase the in-plane crystallite size (La) from 2.184 to 2.64 nm while its transient nature effectively preserves a favorable interlayer spacing (0.371 nm) (d002) (conventional carbonization is 0.361 nm) and stacking height (Lc) a structural outcome that is beneficial for rapid Na⁺ intercalation and high rate performances38.

The four heating parameters create a vast design space (T1: 300-900 °C; t1: 60-120 min; T2: 1000-2200 °C; t2: 1-60 s) wherein material performance is highly sensitive to process variations, resulting in a diverse range of performances: e.g., capacity 100-300 mAh g-1, initial coulombic efficiency (ICE) 30-80% (Fig. 2d, Supplementary Fig. 2, Supplementary Table 2). Therefore, a Gaussian Process Regression (GPR) model coupled with an active learning strategy using an Expected Improvement (EI) acquisition function39-41 (Supplementary Fig. 3) was applied to accelerate optimization of capacity and ICE of Dig-HC under four process parameters: pyrolysis (T1, t1) and PJH carbonization (T2, t2). Our initial analysis revealed moderate and comparable linear correlations for all four process parameters, while a strong linear correlation (R = 0.94) was identified between ICE and capacity (Fig. 2e, Supplementary Fig. 4). This simplifies our approach, whereby the dual-objective optimization was reformulated into a more parsimonious single-objective problem targeting only capacity. Our predictive surrogate model yielded a training R2 of 0.96, demonstrating its high fidelity in representing the performance landscape defined by the chosen data (Fig. 2f).

Our optimization strategy commenced with an analysis of the initial dataset, which identified that the PJH carbonization conditions of T2 >1800 °C are associated with higher capacity in our dataset. We initially fixed the PJH carbonization parameter (T2=1800 ℃; t2=40 s) to focus on optimizing the pyrolysis conditions (T1 and t1) (Supplementary Fig. 5). Upon mapping the parameter space (T1; t1) with the GPR model, we identified T₁=800 °C and t₁=1.5 h as the optimal condition for pyrolysis, considering its higher predicted capacity, lower energy consumption, and alignment with findings in the literatures11, 42, 43. Following T1, t1 determination, the PJH process parameters T2 and t2 were identified as an optimal second-stage temperature (T₂) of 1800 °C and the PJH duration (t2) of 40 s (Fig. 2g, Supplementary Fig. 6). After one iteration, the final model’s R² remains above 0.9, showing the stability of GPR model. The whole parameter space spanned pyrolysis and PJH carbonization, with predictions across 1,453 generated parameter combinations within this extensive matrix (Fig. 2h, Supplementary Fig. 7) facilitating later ML-guided optimization and intelligent manufacturing.

Electrochemical properties
To elucidate the advantages of our ML-guided intelligent carbonization, the resulting Dig-HC was compared against biochar and commercial Kuraray HC, showing higher sodium storage capabilities over the reference carbon negative electrodes. In initial charge-discharge cycles in ester-based electrolytes (Fig. 3a), Dig-HC achieved a high reversible capacity of 369 mAh g-1 and an ICE of 79%, exceeding precursor biochar (150 mAh g-1, 35% ICE) and commercial Kuraray HC (290 mAh g-1, 75% ICE)44, 45. To intuitively analyze the origins of its enhanced capacity, we performed a segmental analysis of the discharge profile (Fig. 3b), which revealed a dominant capacity contribution from the intermediate voltage stage in Dig-HC, delivering a 233.58 mAh g⁻¹. Furthermore, Dig-HC maintains 94.3% capacity retention at 0.2 C after 100 cycles (Fig. 3c), comparing favourably with Kuraray HC and biochar. According to the Electrochemical Impedance Spectroscopy (EIS) profiles in Fig. 3d, Dig-HC exhibited a lower charge-transfer resistance (Rct) of only 23.67 Ω than that of biochar (52.24 Ω) and Kuraray HC (29.98 Ω), indicating an improved diffusion kinetics of Na ions (Supplementary Fig. 8, Supplementary Table 3). Additionally, the Cyclic Voltammetry (CV) analysis shows that Dig-HC has a larger integrated area, indicating a higher reversible capacity, as well as increased peak currents, which correspond to faster reaction kinetics (Supplementary Fig. 9).

The rate capability of Dig-HC was tested in an ether-based electrolyte to assess its performance robustness across different electrolyte systems. Fig. 3e summarizes Dig-HC alongside biochar, Kuraray HC, and representative literatures31, 42, 44-48 HCs under different specific currents. Dig-HC delivers 350 mAh g-1 at 0.2 C and 280 mAh g-1 at 10 C, surpassing biochar, Kuraray HC (Supplementary Table 4). Moreover, in the more challenging carbonate-based electrolyte system, Dig‑HC delivered ~80 mAh g-1 at 10 C—higher than biochar and Kuraray HC (<50 mAh g-1) (Supplementary Fig. 10). This further demonstrates the broad electrolyte-system compatibility of Dig‑HC enabled by our intelligent carbonization strategy. It clearly demonstrates that the contribution from fast, surface-controlled capacitive processes progressively increases from 45% at 0.1 mV s-1 to a dominant 72% at 1.0 mV s-1. This increasing dominance of non-diffusion-limited capacitive charge storage is the fundamental reason for the material’s strong high-rate performance (Supplementary Fig. 11). Regarding low-temperature performance, Dig-HC stabilized at 235.3 mAh g-1 and retained 97% of this capacity after 100 cycles at -40℃. It surpassed Kuraray HC, which delivered a capacity of 225.7 mAh g-1 before it short-circuited at the 17th cycle under identical conditions (Fig. 3f). Overall, Dig-HC demonstrated a robust electrochemical performance across a wide temperature range from -40 to 25°C (Supplementary Fig. 12). Even when the charging-discharging rate increased to 10 C, Dig-HC delivered 280 mAh g-1 and maintained 87.4% capacity retention after 5000 cycles, demonstrating enhanced stability relative to biochar (retained 62.4% after 4000 cycles) and Kuraray HC (short-circuited at 3000th) (Fig. 3g). Furthermore, when used as an negative electrode material in lithium‑ion batteries, Dig‑HC delivers a higher capacity (385 mAh g−1 at 0.1 A g-1) than commercially reported graphite49 (372 mAh g−1 at 0.1 A g-1). It also exhibits better rate capability, retaining approximately 141 mAh g−1 under a high specific current of 1 A g-1 (Supplementary Fig. 13).

Elucidation of structure-property relationships.
Despite achieving optimized Dig-HC performance, a comprehensive, predictive understanding of HC’s intricate structure-property relationships remains largely elusive. We selected XRD as the primary characterization tool, as it provides essential microstructural parameters (e.g., interlayer spacing d002, La, and Lc), with the detailed calculation shown in Supplementary Note 2, which are widely recognized as key factors influencing the performance of HCs (Fig. 4a, Supplementary Fig. 14). Moreover, the rapid, cost-effective, and highly reproducible nature of XRD makes it suited for generating the large datasets necessary to train a robust ML model and later industrial adoption. Conversely, techniques like high-resolution transmission electron microscopy (HRTEM) are ill-suited for large-scale feedback due to their localized sampling, complex preparation, and high operational costs. Moreover, relying on precursor characterization is infeasible, as the substantial evolution in phase and functional groups during carbonization severs the direct link between the starting material’s properties and the final negative electrode performance.

It should also be noted that the integrated areas of the (002) (i.e., A002) and (100) (i.e., A100) XRD peaks—which quantify c-axis stacking and in-plane graphitic order, respectively—are critical structural descriptors that are frequently ignored (Fig. 4b). Seven indices were chosen for subsequent analysis, including six physically meaningful features of d002, the interplanar spacing of the graphite (100) planes d100, Lₐ, Lc, A100, and A002 (Supplementary Table 5) and capacity. To bolster model robustness, extensive literature data on HC structural parameters were compiled (Supplementary Table 6) with our experimental data. Meanwhile, the range of both input structural indices and output capacities (Fig. 4c) is expansive, which underpins the development of a generalizable model capable of robustly identifying the optimal hard carbon structure.

By leveraging the automated feature extraction capabilities of a Multi-Layer Perceptron (MLP) (Supplementary Fig. 14), our model autonomously constructed four interaction features (A100/(A100+A002), N, A100+A002, and A100/A002) from the six primary descriptors, where A100/(A100+A002), named performance correlated factor (PCF), exhibits the strongest positive correlation with capacity (Fig. 4d, Supplementary Fig. 16,17). It reflects the relative contribution of in-plane ordering to the overall degree of order in HC (Supplementary Fig. 18). In other words, it serves as a mesoscale morphological descriptor rather than a direct crystallographic parameter50, 51. Built upon this enriched feature set, the surrogated predictive model demonstrated high accuracy, with R² values surpassing 0.94 on both the training and testing sets (Fig. 4e).

We then employed Shapley additive explanations52 (SHAP) to uncover the intricate, non-linear structure-property relationships within the MLP model, which reveals that the engineered feature, PCF, is the most dominant positive driver (Fig. 4f). It represents the fraction of in-plane graphitic ordering relative to the total crystalline content. Furthermore, the analysis indicates that a combination of a larger La and a smaller Lc is advantageous for Na⁺ storage, which is consistent with our linear correlation analysis (Supplementary Fig. 19). It also clarified the nuanced role of d002, whose positive impact at a localized sweet spot (0.37-0.38 nm), thus reconciling our findings with the broader literature14, 20, 47. SHAP dependence plots (Supplementary Fig. 20) shows PCF and La have strong positive monotonic effects on predicted capacity, while d002 contributes positively within a narrow 0.37–0.39 nm window. Feature interactions indicate that enlarging d002 simply is ineffective, high capacity also demands a large La, and a high PCF. The PJH process notably co-optimizes PCF and La while pinning d002 in the optimal range, enabling the improved sodium storage.

To further corroborate the ML-elucidated structure-property relationships, a suite of additional characterization techniques was employed to compare Dig-HC and biochar samples (Supplementary Table 7, 8). While both samples displayed broad (002) and (100) graphitic carbon peaks in XRD, Dig-HC’s peaks were more intense and exhibited larger integrated areas53. Comparative analysis (Fig. 4g) showed Dig-HC possessed an increased PCF of 0.2 and a larger La of 2.64 nm relative to biochar, signifying a more ordered in-plane structure with larger graphitic domains. This structural enhancement is directly responsible for the increase in its plateau capacity, as it allows for more facile Na⁺ intercalation and pore-filling54. Critically, despite the intense thermal shock, the transient PJH treatment effectively preserved an interlayer spacing of 0.37-0.38 nm in Dig-HC, a range optimal for facilitating efficient Na⁺ intercalation55. Collectively, the intelligent carbonization strategy simultaneously promotes the lateral growth of short-range ordered graphitic domains (enhancing La and PCF) while suppressing their c-axis stacking (maintaining a larger d002 and a smaller Lc), a process wherein the curled edges of the microcrystals form abundant closed pores. These distinct structural attributes affirm that an engineered graphitic microcrystalline framework promotes high-performance sodium storage.

In addition, N2 adsorption-desorption analysis (Supplementary Fig. 21) revealed that the PJH process dramatically reduced the specific surface area (SSA) from 82.48 m2 g-1 for the biochar to 5.48 m2 g-1 for Dig-HC. This reduction is anticipated to curtail parasitic electrolyte reactions, thereby enhancing ICE and reversibility25. Concurrently, the average open pore diameters of biochar and Dig-HC are 2.2 nm and 9.14 nm, respectively. This observation is likely ascribed to the metastable, kinetically-dominated PJH process (< 1 min at ultrahigh temperature). During the rapid heating ramp Lc initially decreased (from 1.05 to 0.75 nm), while a 40 s dwell at peak temperature promoted recrystallization and an increase in La (from 2.18 to 2.64 nm). The subsequent rapid quench caused the thin, laterally large graphite microcrystalline platelets to curl, leading to the formation of larger closed pores. Together, these time-dependent kinetic effects during PJH explain the observed evolution of microstructure and porosity38, 56. Similar rapid synthesis techniques likewise show that employing rapid heating and cooling profiles can produce hard carbon with fewer defects and a richer, more diversified pore structure56. Further Small-Angle X-ray Scattering (SAXS)analysis (Supplementary Fig. 22, 23) elucidated a distinct shoulder in the scattering profile of Dig-HC (the scattering vector (q) range of 0.1-0.4 Å⁻¹, absent in biochar). This indicates the formation of larger, more well-defined closed pores, with the average size increasing from ~0.67 nm to 4.15 nm (Fig. 4h). Such developed closed porosity is believed to facilitate Na cluster formation, contributing to the low-voltage plateau capacity and concurrently bolstering ICE. Meanwhile, the first-cycle CV curves further indicate that this structure is more compatible with ether-based electrolytes than with ester-based ones , exhibiting sharper and higher peak currents and fewer side reactions, which facilitate the formation of a stable solid electrolyte interphase (Supplementary Fig. 24). Although morphological analysis by scanning electron microscopy (SEM) indicated no discernible differences among the three samples (Supplementary Fig. 25), HRTEM provided direct visual evidence for the structural evolution from biochar to Dig-HC (Fig. 4i, 4j, Supplementary Fig. 26). Dig-HC exhibited a more ordered graphitic microcrystalline architecture and a distinct internal porosity, indicating a higher degree of local graphitic ordering. Compared to biochar, Dig-HC possesses larger enclosed nanopores formed by the curling of short-range ordered graphitic micro-crystallites.

Raman spectroscopy57 (Supplementary Fig. 27) indicated that higher PJH temperatures lead to both a slight decrease in the ID/IG ratio (enhanced ordering) and an increase in capacity. According to the X-ray Photoelectron Spectroscopy (XPS) results (Supplementary Table 9), C 1s spectra for Dig-HC revealed a higher proportion of C=C bonds (~284.8 eV), while O 1s spectra showed decreased C=O content (~532.3 eV) (Supplementary Fig. 28). This latter observation signifies effective impurity removal and suggests an increased sp3-carbon proportion as well as a more ordered carbon structure, which is considered beneficial for Na storage58. These results are consistent with the XRD and Raman data, further demonstrating the important role of PCF parameters for the enhanced battery performance.

Practicality and Outlook.
An intelligent manufacturing process (Fig. 5a, Supplementary Table 10, Supplementary Fig. 29) is proposed for highly efficient production of Dig-HC with high performance in real time based on the combination of the transient PJH method, the in-situ XRD characterization, and ML algorithm. In this workflow, the sub-minute (<1 min) PJH platform performs high-throughput synthesis. Concurrently, in-situ XRD extracts key structural features (e.g., PCF, La, d002). Based on our pre-established process-structure-property model, the ML algorithm uses these features to predict battery’s performance, perform inverse design, and generate recommendations for optimal process parameters. These recommendations are immediately fed back to the PJH process, enabling precise and rapid tuning of the HC’s structural features to meet target performance. Ultimately, this intelligent production approach not only replaces labor-intensive battery assembly and testing with rapid, data-driven XRD analysis and ML prediction but also establishes an efficient paradigm for the intelligent manufacturing of advanced HC negative electrodes with consistent and stable performance (Fig. 5b). Dig-HC not only shows enhanced performance than the conventional HC (Con-HC) in terms of capacity, rate, and cycling, but also achieves substantial gains in energy and time efficiency with a much smaller carbon footprint59. We used COMSOL Multiphysics to simulate the temperature distribution of a 100 cm × 60 cm heated substrate. The central processing region exhibits a highly uniform temperature field (Supplementary Fig. 30, Supplementary Table 11), consistent with the stable material quality observed at scale (Supplementary Fig. 31).

The adaptive control feature of our intelligent manufacturing process can be engineered to address the diversity of biomass precursors. For example, despite the profound structural differences between precursors—ranging from highly crystalline cotton (90% cellulose) and complex lignocellulosic peanut shells (45% cellulose) to glucose—our intelligent manufacturing successfully identified a robust optimization route for each, yielding HC capacities in the range of 340-370 mAh g⁻¹ (at 0.2 C) (Fig. 5c). On the other hand, our strategy can effectively achieve product and performance uniformity even from heterogeneous feedstocks. By manipulating the PJH parameters independently, Dig-HCs derived from the three above precursors exhibit a similar microstructure, evidenced by a convergence in their PCF from XRD analysis (Supplementary Fig. 32). As a result, our optimization strategy can consistently deliver consistent and high-capacity HCs stabilized at 340 mAh g-1, regardless of precursor origin (Fig. 5d, Supplementary Table 12). Furthermore, when substituting the input variables with the fundamental lignocellulosic ratios (cellulose, hemicellulose, and lignin), our intelligent carbonization strategy successfully converts these diverse compositions into performance-unified HC negative electrodes (330 mAh g-1) through iterative optimization (Supplementary Table 13, Supplementary Fig. 33). Significantly, the intelligent carbonization establishes a transferable paradigm for materials discovery. By leveraging transfer learning60 to freeze universal structure-property layers, the model can be rapidly adapted to updated multi-ion systems with minimal experimental data, enabling the efficient inverse design of bespoke materials for next-generation energy storage.

We performed a comprehensive techno-economic analysis (TEA) and life cycle assessment (LCA) of our intelligent carbonization strategy (Fig. 5e, 5f, Supplementary Table 14). Detailed analysis procedures, assumptions, and input parameters are described in Supplementary Note 3 and Supplementary Note 4. Specifically, our strategy reduces the carbon footprint from the carbonization stage by a factor of 14 and the overall costs by a factor of 30 relative to conventional carbonization. This leads to a 16-fold reduction in overall lifecycle emissions and an 8-fold reduction in total development cost, establishing a scalable blueprint where improved performance is achieved in concert with, not at the expense of, economic and ecological sustainability. From a life-cycle perspective, we establish a holistic and sustainable life cycle for advanced HC from biomass (Fig. 5g). The cycle starts with abundant and renewable biomass, which serves as a carbon-neutral and sustainable feedstock. This raw material is then transformed via our intelligent carbonization strategy, where energy-efficient and electrified PJH33 is guided by ML to minimize energy waste and consumption in producing high-performance and low-cost HC negative electrodes. The resulting HC then enables durable and long-life SIBs for sustainable energy storage applications. This sustainable cycle consists of renewable materials, electrified synthesis, and clean energy storage, representing a holistic, full-lifecycle approach to sustainable energy technology.

Methods
Chemical and materials.
Cellulose powder (97%, ≤25 μm, Innochem, A06413, (C₆H₁₀O₅)ₙ) was used as precursor. Cotton (degreased absorbent cotton; Labshark; purity 99%), peanut shells (purchased from Tan’ernuo; purity 90%), and glucose (Macklin; purity 98%) were used as biomass precursors. Acetylene black, polyvinylidene fluoride (Solef, PVDF 5130, DP = (1.0-1.2) × 106), Cu collector (purity ≥ 99.9%, thickness 9 μm) and CR2032 cell cases were acquired from Shenzhen Ke Jing Zhi Da Technology Co., Ltd. N-Methylpyrrolidone (NMP, purity ≥ 99%) were purchased from Aladdin. Organic electrolyte (ethylene carbonate/dimethyl carbonate (EC/DMC = 1:1 by volume) or diethylene glycol dimethyl ether (DIGLYME)) were purchased from DoDoChem. All reagents were used as received without further purification.

Material preparation.
All HC samples were prepared from cellulose pyrolysis (Innochem, microcrystalline powder) or complex biomass precursors (cotton, peanut shell, glucose) in two steps. Both steps of the heat treatment were conducted in an argon atmosphere. During the first stage of pyrolysis in a tubular furnace, cellulose powder was heated from room temperature to 800 °C at a rate of 5 °C min-1 and held at 800 °C (T1) for 90 minutes (t1) before cooling naturally to room temperature to form biochar. In the second step, PJH carbonization was performed using the programmable Joule heating method, rapidly heating to 1800 °C (T2) within 1 second and maintaining it for 20 s (t2), repeating this operation once. The HC material obtained by this method was named Dig-HC.

Materials characterization.
Scanning electron microscope (SEM, Zeiss Sigma 300) and transmission electron microscope (TEM, Tecnai G2 F30) were used to obtain information on microstructure. The phase was identified by XRD-7000 (Shimadzu, Japan) with a scanning rate of 10 ° min-1 (Cu K radiation, λ =1.5406 Å). Raman spectra were obtained by a WITEC alpha-300R, Germany. Pore distribution was tested by Xeuss 3.0 UHR, Xenocs. X-ray photoelectron spectroscopy (XPS, Thermo Scientific K-Alpha) was employed to analyze the chemical state of C, O and N.

Electrochemical measurements.
The negative electrode slurry was prepared by mixing 80 wt.% active material (Dig-HC) with 10 wt% acetylene black (Denka black, Denki Kagaku Kogyo; Average particle size was 20-40 nm) and 10 wt.% PVDF in N-methyl-2-pyrrolidone (NMP). The amount of NMP was fixed at 5 μL per mg of active material (e.g., 400 μL NMP for 80 mg active material). The mixture was stirred for 12 h at 26 ± 1 °C, and the resulting slurry was coated onto a single-sided copper foil current collector (purity 99.9%, thickness 9 μm) using an automatic coating machine. The prepared electrodes were dried overnight under vacuum at 120°C. The subsequent product was then cut into electrode sheets with a diameter of 12 mm using a disk cutter (Shenzhen Kejing, MSK-T10), and the loading mass of the active material was approximately 1-2 mg cm-2. A 0.4 mm sodium metal (diameter 14 mm, DoDoChem, stored in an Ar-filled glovebox (H2O and O2 levels both < 0.01 ppm) for no longer than one month before use) as the counter electrode and glass fiber (Whatman GF/A CAT. No.1820-090, diameter 16 mm, thickness 260 μm, pore size 1.6 μm, porosity 40%) as the separator, within an argon-filled glove box. The 1 M NaPF6 solution in ethylene carbonate/dimethyl carbonate (EC/DMC = 1:1 by volume) or diethylene glycol dimethyl ether (DIGLYME) was used as the electrolyte, and the amount is 120 μL. Charge and discharge measurements were conducted in a climatic chamber (25 ± 0.5 °C) using a Neware multi-channel battery testing system (CS3104).

In cycling test, the cells were tested from 2 V to 0.004 V with a specific current of 0.2 C or 10 C. In the low-temperature half-cell test, the temperature was set to -20 °C or -40 ℃, while all other conditions remained unchanged. CV curves were obtained with a scan rate of 0.1 mV s-1. The potentiostatic EIS measurement was conducted using an electrochemical workstation (CS6, Corrtest, Wuhan) in the frequency range 0.1 Hz-100 kHz with a signal amplitude of 5 mV. A total of 50 points were collected within the test frequency range. A quasi-stationary potential was applied for 600 s before carrying out the EIS measurement.

Machine learning models.
To quantitatively map the synthesis-structure-property relationships of the hard carbon, we developed a suite of machine learning models. First, a Gaussian Process Regression (GPR) model was established to predict the final specific capacity directly from four heating process parameters (designated T1, t1, T2, and t2). In parallel, a MLP, incorporating Dropout and L2 regularization and optimized via grid search, was trained to model the link between six key structural parameters and specific capacity.

Our GPR model was constructed using a Radial Basis Function (RBF) kernel as the covariance function, a standard and robust choice for modeling smooth response surfaces. The specific kernel was set as kernel = 1.0 * RBF (length scale=1.0); The primary advantages of the RBF kernel are its versatility and smoothness. As a stationary kernel, it is highly effective at capturing the smooth, non-linear response surfaces characteristic of materials properties, such as the capacity in this work. Its non-parametric nature allows it to flexibly fit complex functional forms without requiring a priori assumptions about the underlying mathematical relationship.

Our optimization strategy uses a closed-loop active learning workflow that couples data acquisition, feature extraction and surrogate modelling with experimental validation. The key step is the choice of the next experimental candidate. To make this decision, the algorithm updates the surrogate after each measurement and uses both the predicted performance and its associated uncertainty to steer the search—prioritizing promising regions while still probing less-sampled areas where uncertainty is higher. To implement this, we utilized Bayesian Optimization coupled with an Expected Improvement (EI) acquisition function. The EI metric is particularly effective for this dual-objective task as it simultaneously evaluates the probability of outperforming the current best result and the potential magnitude of that improvement. The EI is calculated as follows:

EI(x) = (μ(x) - f(x+)) Φ(Z) + σ(x) φ(Z) (1)

where μ(x) and σ(x) correspond to the predictive mean and standard deviation of the GPR model. f(x+) indicates the highest capacity observed to date. ξ is a tuning parameter that governs the balance between exploitation and exploration, for which we adopted the recommended default value of 0.01. Z = (μ(x) - f(x+) - ξ) / σ(x). Φ and φ represent the standard normal Cumulative Distribution Function and Probability Density Function, respectively. During each active learning loop, the model targets the candidate x* that maximizes the EI function, thereby guiding the experimental pathway toward the most promising unobserved regions.

Small-angle X-ray scattering.
SAXS measurements were carried out using a Xenocs Xeuss 3.0 system equipped with a Cu Kα micro-focus X-ray source (λ = 1.5419 Å) operated at 30 W. The scattering signals were recorded by a Pilatus 3R 300K detector (Dectris) with a pixel size of 172 μm. The sample-to-detector distance was set to approximately 200 mm to cover the scattering vector (q) range of interest (0.001–1.0 Å-1). Samples were loaded into capillaries for transmission mode acquisition. The 2D scattering patterns were azimuthally integrated to 1D curves, followed by background subtraction and transmission correction using the instrument’s standard software package.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents “intelligent carbonization,” which transforms diverse biomass feedstocks into unified high-performance hard carbon anodes by integrating programmable Joule heating with predictive machine learning. The authors also introduced a new structural descriptor, the performance-correlated factor (PCF), and revealed its predictive role for electrochemical performances. The ML-optimized hard carbon exhibits outstanding capacity, high rate, and an ultralong cycle life, along with significant potential in energy efficiency. This paper is of significant importance in addressing the long-standing challenge of biomass diversity in its valorization. To further enhance the scientific rigor and impact of this work, I offer the following points for the authors' consideration during revision.\n1. After the sub-minute PJH treatment, the specific surface area (SSA) dramatically decreases while the average sizes of both open and closed pores increase. The underlying physical mechanism for such a drastic structural rearrangement is somewhat underexplored.\n2. The manuscript identifies the PCF as a core discovery, demonstrating its importance in capacity prediction via SHAP analysis. While its correlation with performance is well-established, its physical origin requires a more in-depth explanation. What does the PCF physically represent, and how is it different from the traditional descriptors?\n3. How can the excellent performance and high uniformity achieved at the laboratory scale be maintained during scaled-up production to the kilogram or even ton level? The authors should at least simulate this possibility for large-scale production.\n4. The manuscript utilizes a carbonate-based electrolyte for assessing initial capacity and cycling stability but switches to an ether-based electrolyte when evaluating rate performance. This raises a question: to what extent is the exceptional rate capability of the Dig-HC material attributable to its intrinsic microstructure, versus the optimization of the electrolyte system?\n5. Figures 1c and 2b are key to showcasing the significant energy-saving of this work, highlighting an additional energy input of only 0.1 kWh g⁻¹. However, the manuscript does not provide a detailed explanation of how this value was calculated.\n6. A central conclusion is that the intelligent carbonization strategy can \"unify\" hard carbons from different precursors (cotton, peanut shell, glucose), leading to a consistent performance. Can this approach also handle mixed biomass feedstocks?\n7. A previous report (PNAS, 2021, 118, e2111119118. DOI:10.1073/pnas.2111119118) about ultrafast synthesis of hard carbon anode for Na-ion battery is suggested to added for discussion or comparision, which also adopted the Joule heating.", "reviewer_2": "Major Revision\nThis paper proposes an \"intelligent carbonization\" strategy that integrates programmable Joule heating and machine learning. After analyzing over a thousand synthetic pathways, a performance-correlated factor (PCF) derived from XRD is discovered, which can accurately predict capacity. This strategy converts biochar into high-performance Dig-HC with extremely low energy consumption (reversible capacity of 369 mAh g-1, 280 mAh g-1 at 10C, over 5000 cycles and excellent low-temperature performance). It can also transform various biomasses into hard carbon anodes with uniform performance, providing a solution for biomass valorization and sustainable energy storage. Here are some suggested changes to the manuscript:\n1.From the perspective of energy storage technology iteration, Dig-HC has demonstrated excellent performance in sodium-ion batteries. Could it be extended to potassium-ion batteries, lithium-ion batteries (especially in fast-charging scenarios), or hybrid-ion batteries in the future? Are there new evolutionary laws in its structure-property relationships across multi-ion systems, and can the methodology of this study be transferred to guide material design for multi-ion energy storage systems?\n2.Currently, the input of the machine learning model only includes heating process parameters, without integrating the chemical information of biomass precursors (such as elemental composition and functional group distribution). How to construct a multi-source input fusion model that incorporates both the intrinsic properties of biomass and process parameters as inputs to achieve more universal structure-performance prediction?\n3.Regarding the interpretability of the machine learning model's prediction results, can tools such as SHAP (SHapley Additive exPlanations) or Partial Dependence Plots be used to quantify the contribution of each input feature (process parameters, structural parameters) to the prediction results, thereby providing more explicit physical guidance for experimental design?\n4.For the specific capacity prediction using the Gaussian Process Regression (GPR) model, what is its predictive stability under small-sample datasets? Is it necessary to introduce Bayesian optimization or ensemble learning strategies to further improve the model's predictive accuracy in the edge regions of the process parameter space?\n5.Dig-HC exhibits excellent rate performance in both ester-based and ether-based electrolytes. What are the differences in the interaction mechanisms between the electrolyte solvation structure and the surface/pore structure of Dig-HC? Could the authors further clarify the interface matching rules between the electrolyte and the electrode with the aid of characterization techniques?\n6.What are the specific differences in the XRD-characterized parameters (PCF, La and d002) between Dig-HC and biochar? How do these differences directly affect their sodium storage capacities?\n7.XRD-derived PCF, Raman-derived I_D/I_G ratio, and XPS-measured C=C bond proportion all reflect the ordering degree of materials. What are the advantages and limitations of these three characterization techniques in quantitatively describing the graphitization degree of hard carbon, respectively? How to establish the quantitative conversion relationship between them?\n8.In the intelligent manufacturing process of Dig-HC, what roles do in-situ XRD, PJH, and machine learning play respectively in the \"process-structure-performance\" chain? Please briefly explain the synergistic mechanism of the three in combination with Fig. 5a.\n9.Regarding the convergence of structural parameters in Fig. 5d, Dig-HCs derived from cotton, peanut shells, and glucose exhibit structural convergence in PCF, La and d002. From the perspective of the stage evolution of \"precursor pyrolysis-graphitization\" during carbonization, what common mechanisms exist among the three in terms of graphite nucleation growth rate or other aspects during the PJH stage?\n10.We kindly ask the authors to check the English expressions in the manuscript. For instance, \"a increased PCF\" in Line 2 of Page 11 should be corrected to \"an increased PCF\" (since \"increased\" starts with a vowel sound, the indefinite article \"an\" is grammatically appropriate here).", "reviewer_3": "The study titled \"Data-driven intelligent carbonization unifies diverse biomass into high-performance hard carbon anodes\" by Cui et al. presents an active learning-driven strategy to optimize capacity of biomass-derived hard carbons. This work is of significant value to the battery community as it provides a promising solution to scaling of cheap and widely available biomass-derived synthesis of hard carbon anodes. I do have a few comments which the authors should take care of before accepting it for publication (minor revision):\n1. SHAP dependence plots for important features like PCF should also be plotted to check the trend of capacity as a function of these features. The authors should also make a comment on whether the trends are in line with expected behavior.\n2. I am a bit lost on the difference between GP-driven active learning and two other MLP developed for predicting specific capacity and structural parameters. It is not cleary explained in the draft why is there a need for other two MLPs.\n3. Can authors comment on whether any directmaterial structure-based features can be used instead of XRD-derived features which will limit the screening of biomass on a large scale?\n4. Details of the active learning framework is also missig, for example, which covariance kernel was used, how many experiment feedback-active learning iterations were carried in this study, etc."}, "author_response": "Point-by-Point Response\n(Black type: Reviewer’s comments; Blue type: Our response; Red type: Our revision)\nReviewer #1\nThis manuscript presents “intelligent carbonization,” which transforms diverse biomass feedstocks into unified high-performance hard carbon anodes by integrating programmable Joule heating with predictive machine learning. The authors also introduced a new structural descriptor, the performance-correlated factor (PCF), and revealed its predictive role for electrochemical performances. The ML-optimized hard carbon exhibits outstanding capacity, high rate, and an ultralong cycle life, along with significant potential in energy efficiency. This paper is of significant importance in addressing the long-standing challenge of biomass diversity in its valorization. To further enhance the scientific rigor and impact of this work, I offer the following points for the authors' consideration during revision.\nResponse: Thank you very much for your positive and constructive comments on our manuscript. To further enhance the scientific rigor and impact of this work, detailed point-to-point responses to the reviewer’s question are shown below.\nComment #1. After the sub-minute PJH treatment, the specific surface area (SSA) dramatically decreases while the average sizes of both open and closed pores increase. The underlying physical mechanism for such a drastic structural rearrangement is somewhat underexplored.\nResponse: We thank the reviewer for highlighting this important point. We have substantially expanded the mechanism discussion in revised manuscript. The decrease in SSA accompanied by the enlargement of both open and closed pores after the sub-minute PJH treatment (Fig. R1a) arises from a kinetically driven, multi-stage structural reconstruction, as outlined below.\n(1) Geometric origin. The SSA reduction is a direct consequence of two coupled geometric transformations: collapse of micropore volume and expansion of pore diameter.\n2V\nSSA=R\nwhere, V is the micropore volume and R is the pore diameter. The micropore volume drops from 0.031 to 0.0016 cm³ g⁻¹ (Fig. R1b), while the average open-pore diameter increases from 2.2 to 9.14 nm. Pore size distributions (Fig. R1c-d) show a transition from biochar dominated by <10 nm micropores (>95%) to Dig-HC centered around ~20 nm with only ~20% micropores. This shift from a microporous to a mesoporous architecture inherently reduces SSA.\nFigure R1. Changes in structural parameters for biochar and Dig-HC of a, pore structure. b, micropore volume. c, the distribution of pore width. d, the distribution of pore area.\n(2) Physical origin. The rapid heating fractures the pre-existing disordered graphitic stacks (Lc decreases from 1.06 to 0.75 nm), while the short isothermal stage promotes lateral growth of micro-crystallites along the a-axis (La increases from 2.18 to 2.64 nm). The subsequent quench—from ~1800°C to room temperature in <5 s (Fig. R2a–c)—induces curling and reorganization of these short-range ordered domains. This dynamic restructuring collapses and coalesces the micropore network into larger pores. This mechanism is consistent with our prior PJH observations (Joule, 2025, 9, 3, 101812) and align with independent studies (PANS 2021, 118, 42, e2111119118).\nFigure R2. a, The evolution of graphitic micro-crystallite structural parameters during PJH process. b, Changes in the size of closed pores and in La and Lc for biochar and Dig-HC.\nOur revision:\n1. Added detailed description and references.\np 12, line 12-17\nThis observation is likely ascribed to the metastable, kinetically-dominated PJH process (< 1 min at ultrahigh temperature). During the rapid heating ramp Lc initially decreased (from 1.05 to 0.75 nm), while a 40 s dwell at peak temperature promoted recrystallization and an increase in La (from 2.18 to 2.64 nm). The subsequent rapid quench caused the thin, laterally large graphite microcrystalline platelets to curl, leading to the formation of larger closed pores. Together, these time-dependent kinetic effects during PJH explain the observed evolution of microstructure and porosity38, 60.\n2. Added figures.\nSupplementary Fig. 20 Open-pore structural characterization. a, Nitrogen adsorption–desorption isotherms. b, BJH Adsorption d V/d log(D) Pore Volume. c, DFT pore size distributions for HCs. d, micropore volume distribution. e, micropore volume. f, the distribution of pore width. g, the distribution of pore area.\nComment #2. The manuscript identifies the PCF as a core discovery, demonstrating its importance in capacity prediction via SHAP analysis. While its correlation with performance is well-established, its physical origin requires a more in-depth explanation. What does the PCF physically represent, and how is it different from the traditional descriptors?\nResponse: We thank the reviewer for the insightful question regarding the physical meaning of PCF and its distinction from conventional structural descriptors. As defined in the manuscript, PCF is extracted from the XRD patterns of hard carbon as the ratio between the integrated area of the (100) peak and the total integrated peak area (Fig. R3a), and therefore functions as a mesoscopic morphological descriptor.\nPhysically, PCF statistically quantifies the relative dominance of in-plane graphitic ordering (2D aromatic continuity) versus c-axis stacking (3D graphitization) within the hard carbon matrix, a feature identified in previous work (Adv. Phys. 1986, 35, 317-374). A higher PCF indicates microstructures with laterally well-developed aromatic sheets (Nature 2024, 634, 80–84) that remain thinly stacked and turbostratic—reflecting a preference for 2D sheet extension over 3D stacking (Fig. R3b, c).\nFigure R3. Schematic diagram of the structural parts of graphite microcrystalline.\nDifferences with traditional descriptors: Traditional descriptors such as La, Lc and d002 are crystallographic constants obtained from peak broadening and positions in XRD; they describe the absolute crystallite dimensions (La: lateral domain size; Lc: stacking height) (Adv. Mater. 2023, 35, e2302613). In contrast, PCF is not a size metric; It is an engineering feature derived from integrated intensities that captures the relative extent of in-plane order within the total crystalline ordering, thereby reflecting material organization and the degree of turbostratic disorder.\nOur revision:\n1. Added detailed description and references.\np 11, line 2-5\nIt reflects the relative contribution of in-plane ordering to the overall degree of order in HC. In other words, it serves as a mesoscale morphological descriptor rather than a direct crystallographic parameter. Built upon this enriched feature set, the surrogated predictive model demonstrated exceptional accuracy, with R² values surpassing 0.94 on both the training and testing sets (Fig. 4e).\np 25, line 1-2\n2. Added figures.\nSupplementary Fig. 17 Schematic diagram of the structural parts of graphite microcrystalline.\nComment #3. How can the excellent performance and high uniformity achieved at the laboratory scale be maintained during scaled-up production to the kilogram or even ton level? The authors should at least simulate this possibility for large-scale production.\nResponse: We thank the reviewer for raising this important question regarding scale-up. To evaluate the feasibility of maintaining performance and uniformity beyond the laboratory scale, we conducted both experimental validation and thermal-field simulations.\nFirst, we employed our previously reported laboratory roll-to-roll apparatus to demonstrate continuous PJH processing (Fig. R4a). A height-adjustable scraper sets the precursor thickness to 1 mm, while an 8 cm-wide carbon-felt conveyor transports the biochar through a 10 cm × 6 cm carbon-felt heating zone powered at 38 V and 32 A (~1 kW). With a belt speed of 9 cm/min, the system delivers a throughput of ~312 g/h (Table R1). Randomly collected samples from three spatial positions of the resulting Dig-HC show no performance degradation relative to the bench scale, all reaching 330–340 mAh g-1 at 0.2 C (Fig. R4b).\nFigure R4. a, Laboratory setup of a small-scale roll-to-roll heating device. b, Charge-discharge curves of three different batches of cellulose-derived hard carbon from a lab-scale roll-to-roll setup.\nTable R1. Data of yield calculation\nParameter\nCurrent/ A 32\nPotential/ V 38\nTemperature/ ℃ 1800\nPower/ W 1216\nHeating size/ cm 10*6\nProcessing speed/cm min-1 9\nYield/ g h-1 312\nTo further investigate thermal uniformity at a larger scale, we utilized COMSOL Multiphysics to simulate the thermal field distribution (Figure R5a). The simulations indicate a highly uniform temperature field across the central processing region of the sample, while localized temperature drops occur near the electrodes due to edge effects (Figure R5b). In the actual device design, we specifically configured the conveyor belt width to be slightly narrower than the heating source length. This geometric arrangement ensures that biochar passes exclusively through the uniform temperature zone, thereby guaranteeing uniform product during scaled-up manufacturing.\nFigure R5. a, The sample is a 2D model with dimensions of 100cm in length and 60cm in height. The left and right ends serve as positive and negative electrodes, respectively, with a width of 20cm and a height of 60cm. The positive electrode is connected to a potential of 60V, while the negative electrode is grounded. The top and bottom are composed of quartz. b, Temperature distribution of joule heating in COMSOL simulations.\nOur revision:\n1.Added detailed description and references.\np 15, line 12-15\nDig-HC (red area) not only outperforms the conventional HC benchmark (blue area) in terms of capacity, rate, and cycling, but also achieves radical gains in exceptional energy and time efficiency with a much smaller carbon footprint61. We used COMSOL Multiphysics to simulate the temperature distribution of a 100 cm × 60 cm heated substrate. The central processing region exhibits a highly uniform temperature field (Supplementary Fig. 29, Supplementary Table. 10), consistent with the stable material quality observed at scale.\n2.Added data and figures.\nSupplementary Fig. 29 COMSOL simulation model of joule heating. a, The sample is a 2D model with dimensions of 100 cm in length and 60 cm in height. The left and right ends serve as positive and negative electrodes, respectively, with a width of 20 cm and a height of 60 cm. The positive electrode is connected to a potential of 60 V, while the negative electrode is grounded. The top and bottom are composed of quartz. b, Temperature distribution of joule heating in COMSOL simulations.\nSupplementary Fig. 30 Charge-discharge curves of three different batches of cellulose-derived hard carbon from a lab-scale roll-to-roll setup.\nComment #4. The manuscript utilizes a carbonate-based electrolyte for assessing initial capacity and cycling stability but switches to an ether-based electrolyte when evaluating rate performance. This raises a question: to what extent is the exceptional rate capability of the Dig-HC material attributable to its intrinsic microstructure, versus the optimization of the electrolyte system?\nResponse: We appreciate the reviewer’s thoughtful comment. The use of two electrolyte systems was intentional, designed to assess the robustness of Dig-HC across distinct electrochemical environments. Carbonate electrolytes were employed to enable direct comparison with prior studies, as they remain the dominant choice in practical high-rate batteries; Ether-based electrolyte was additionally used to evaluate the fast-charging and rate performances due to its easy de-solvation behavior. Notably, our Dig-HC performs better than conventional HC anodes at high rates in both electrolytes.\nOrigin of high performance. The exceptional rate capability originates from the intrinsic microstructure of Dig-HC—specifically its high PCF and well-developed closed porosity—rather than from electrolyte-specific optimizations. To substantiate this, we added rate-performance data obtained entirely in carbonate ester–based electrolytes. Even at 3 A g-1, Dig-HC delivers 62 mAh g-1, far exceeding commercial Kuraray HC (36 mAh g-1) and biochar (28 mAh g-1) (Fig. R6b). This confirms that the high-rate performance persists independent of the electrolyte formulation.\nFurthermore, benchmarking these carbonate-electrolyte results against the literature (Energy Environ. Mater. 2023, 6, e12523; Angew. Chem. Int. Ed. 2025, 64, e202424028; Adv. Funct. Mater. 2022, 32 2209523; Angew. Chem. Int. Ed. 2025, 64, e202425507) shows that Dig-HC remains among the top-performing hard carbons (Fig. R6c). These results collectively support our conclusion that the superior rate capability is primarily governed by the material’s intrinsic structural features. Collectively, these results demonstrate that the superior rate capability of Dig-HC is intrinsically structure-driven rather than electrolyte-dependent.\nFigure R6. Comparison of rate performance for different HCs in a, ether-based electrolyte and b, c, carbonate ester system, proving the superior performance is orginated mostly from the unique structure in our Dig-HC.\nOur revision:\n1. Added detailed description and references.\np 8, line 20-23\nThe rate capability of Dig-HC was tested in an ether-based electrolyte to assess its performance robustness across different electrolyte systems. It delivers 350 mAh g-1 at 0.2 C and 280 mAh g-1 at 10C, surpassing biochar, Kuraray HC, and many literature-reported HCs14, 45-51 (Fig. 3e, Supplementary Table 3). Moreover, in the more challenging carbonate-based electrolyte system, Dig‑HC outperforms the control samples, delivering ~80 mAh g-1 at 10 C—higher than biochar and Kuraray HC (<50 mAh g-1) (Supplementary Fig. 9). This further demonstrates the broad electrolyte-system compatibility of Dig‑HC enabled by our intelligent carbonization strategy.\n2. Added data and figures.\nSupplementary Fig. 9. a, Cyclic Voltammetry (CV) curves of Dig-HC recorded at 0.1 mV s-1 for the first three cycles. b, Rate performance for different HCs.\nComment #5. Figures 1c and 2b are key to showcasing the significant energy-saving of this work, highlighting an additional energy input of only 0.1 kWh g⁻¹. However, the manuscript does not provide a detailed explanation of how this value was calculated.\nResponse: We appreciate the reviewer’s request for clarification. The reported value of 0.1 kWh g⁻1 was calculated by integrating the electrical power (P) recorded by the power supply over the PJH processing time (t) and normalizing by the mass (m) of the obtained product:\nP t\nE(kWh g⁻¹)=\nm\nIn a representative synthesis, a power input of ~900 W was maintained for ~40 s to achieve a temperature of 1800°C. This run, utilizing a 2x6 cm carbon cloth substrate, produced a typical yield of ~100 mg of Dig-HC. This operational sequence corresponds to a calculated energy consumption of ~0.11 kWh g-1. At larger scales, the energy consumption is anticipated to be even lower, considering the implementation of heat exchange systems and the contribution of the material’s own exothermic heat release at high temperatures.\nOur revision:\n1.Added detailed description.\nSupplementary Information p 30 line 2-9\nCalculation formula for energy consumption:\nThe energy consumption was calculated by converting the power output (P) displayed on the power supply unit over the processing time (t), and subsequently normalizing this value by the mass (m) of the resulting Dig-HC. The specific equation used for this calculation is as follows:\nP t\nE(kWh g⁻¹)=\nm\nThe specific energy consumption was calculated from a representative synthesis. During this process, a power input of ~900 W was maintained for ~40 s to achieve a temperature of 1800°C. This run, utilizing a 2x6 cm carbon cloth substrate, produced a typical yield of ~100 mg of Dig-HC. This operational sequence corresponds to a calculated energy consumption of ~0.11 kWh g-1.\nComment #6. A central conclusion is that the intelligent carbonization strategy can \"unify\" hard carbons from different precursors (cotton, peanut shell, glucose), leading to a consistent performance. Can this approach also handle mixed biomass feedstocks?\nResponse: We thank the reviewer for this highly practical question. In principle, consistent electrochemical performance can indeed be achieved from mixed biomass feedstocks, provided that the mixture is compositionally homogeneous and the component ratios remain stable within a batch. We note, however, our system cannot yet ensure full consistency when the feedstock composition fluctuates dynamically in real time. Achieving real-time adaptive manufacturing that autonomously compensates for varying raw-material inputs remains an important direction for future development.\nTo systematically evaluate the feasibility of mixed-feedstock processing, we formulated precursors by blending cellulose, hemicellulose, and lignin in three distinct ratios (Table R2), guided by our ML framework. Samples are denoted as CxHyLz, where x, y, and z represent the respective component fractions in units of 10 wt% (e.g., C1H2L7 = 10 wt% cellulose, 20 wt% hemicellulose, 70 wt% lignin). Using rapid PJH synthesis, we generated a series of HCs spanning diverse structures (Fig. R7). The MLP model was applied to predict capacity and identify, for a given compositional class, precursor formulations and structural attributes that maximize performance. These predicted optima were then passed to a GPR model to efficiently locate the corresponding processing window. As a result, precursor mixtures with similar component ratios could be tuned to yield nearly identical electrochemical performance (~330 mAh g⁻¹). XRD analysis further confirmed that the key structural descriptors of the optimized samples—PCF, La, and d002—were closely aligned.\nThese findings demonstrate that our intelligent carbonization strategy can indeed unify mixed biomass feedstocks, provided compositional homogeneity is maintained.\nTable R2. Dig-HC samples derived from varying ratios of cellulose, hemicellulose, and lignin.\nSample cellulose hemicellulose lignin\nC1H2L7 10wt% 20wt% 70wt%\nC3H5L2 30wt% 50wt% 20wt%\nC5H1L4 50wt% 10wt% 40wt%\nC7H2L1 70wt% 20wt% 10wt%\nFigure R7. a, X-ray diffraction (XRD) patterns of four samples with different composition ratios. b, Initial charge–discharge profiles. c, Consistency of electrochemical performance and structural parameters among four optimized precursor compositions.\nOur revision:\n1. Added detailed description.\np 15, line 26-27; p 16, line 1-6\nFurthermore, when substituting the input variables with the fundamental lignocellulosic ratios (cellulose, hemicellulose, and lignin), our intelligent carbonization strategy successfully converts these diverse compositions into performance-unified HC anodes (330 mAh g-1) through iterative optimization. Significantly, the intelligent carbonization establishes a transferable paradigm for materials discovery. By leveraging transfer learning64 to freeze universal structure-property layers, the model can be rapidly adapted to novel multi-ion systems with minimal experimental data, enabling the efficient inverse design of bespoke materials for next-generation energy storage.\n2. Added data and figures.\nSupplementary Fig. 32 a, X-ray diffraction (XRD) patterns of four samples with different composition ratios. b, Initial charge–discharge profiles. c, Consistency of electrochemical performance and structural parameters among four optimized precursor compositions.\nSupplementary Table 12. Dig-HC samples derived from varying ratios of cellulose, hemicellulose, and lignin.\nSample cellulose hemicellulose lignin\nC1H2L7 10wt% 20wt% 70wt%\nC3H5L2 30wt% 50wt% 20wt%\nC5H1L4 50wt% 10wt% 40wt%\nC7H2L1 70wt% 20wt% 10wt%\nComment #7. A previous report (PNAS, 2021, 118, e2111119118. DOI:10.1073/pnas.2111119118) about ultrafast synthesis of hard carbon anode for Na-ion battery is suggested to added for discussion or comparison, which also adopted the Joule heating.\nResponse: We thank the reviewer for drawing our attention to this valuable PNAS study. We have now added an explicit discussion and comparison in the revised manuscript.\nOur revision:\n1.Added detailed description and references.\np 12, line 17-19\nSimilar ultrafast synthesis techniques likewise show that employing rapid heating and cooling profiles can produce hard carbon with fewer defects and a richer, more diversified pore structure60.\nWe sincerely thank you for your constructive comments and careful evaluation of our work. We hope that the substantial revisions and new analyses provided in this response satisfactorily address all of your concerns.\nReviewer #2\nThis paper proposes an \"intelligent carbonization\" strategy that integrates programmable Joule heating and machine learning. After analyzing over a thousand synthetic pathways, a performance-correlated factor (PCF) derived from XRD is discovered, which can accurately predict capacity. This strategy converts biochar into high-performance Dig-HC with extremely low energy consumption (reversible capacity of 369 mAh g-1, 280 mAh g-1 at 10C, over 5000 cycles and excellent low-temperature performance). It can also transform various biomasses into hard carbon anodes with uniform performance, providing a solution for biomass valorization and sustainable energy storage. Here are some suggested changes to the manuscript:\nResponse: We sincerely thank the reviewer for their comprehensive summary and highly positive evaluation of our work. We have carefully considered all your suggested changes and have incorporated them into the revised manuscript to further enhance its scientific rigor and clarity. Our detailed, point-by-point responses below.\nComment #1. From the perspective of energy storage technology iteration, Dig-HC has demonstrated excellent performance in sodium-ion batteries. Could it be extended to potassium-ion batteries, lithium-ion batteries (especially in fast-charging scenarios), or hybrid-ion batteries in the future? Are there new evolutionary laws in its structure-property relationships across multi-ion systems, and can the methodology of this study be transferred to guide material design for multi-ion energy storage systems?\nResponse: We thank the reviewer for this insightful and forward-looking question regarding the broader applicability of our work. Indeed, Dig-HC demonstrates significant potential for fast-charging applications due to its unique microstructures.\nExtended to lithium-ion batteries (LIBs): Follow your suggestions, we tried our Dig-HC in LIBs. The electrochemical performance in LIBs (Fig.R1) reveals a predominantly sloping charge-discharge profile, with over 87.5% of the capacity delivered above 0.1 V. This voltage profile suggests a storage mechanism dominated by rapid surface adsorption rather than diffusion-limited intercalation, effectively mitigating lithium plating risks at high rates. Consequently, Dig-HC retains a capacity of 141 mAh g-1 at a high current density of 1 A g-1, surpassing the 115 mAh g-1 observed for commercial graphite (Carbon Energy, 2024, 6, e395). Furthermore, during long-term cycling at 0.1 A g-1, it delivers an average capacity of 385 mAh g-1, exceeding the commercial graphite (372 mAh g-1).\nFigure R1. a, Initial charge–discharge profiles. b, Rate capability. c, Long-term cycling performance at 0.1 A g-1.\nMethodology transfer. We also recognize that the structure–property relationships identified in this work are tailored to the “adsorption–insertion” mechanism for sodium storage, which may not be best suitable for Li- and K-ion storage. Regarding potassium-ion or multi-ion systems, the larger ionic radii of these charge carriers necessitate anode materials with expanded interlayers and robust microcrystalline frameworks to facilitate insertion. Dig-HC, characterized by its expanded interlayer spacing (~0.37 nm), inherently meets these structural criteria.\nTherefore, by redefining the structural descriptors and by applying transfer learning, the process–structure–property model can be reconstructed for Li-ion, K-ion, or hybrid-ion systems building on their own data. In this way, our intelligent carbonization framework provides a generalizable route for accelerated materials design across multi-ion energy storage technologies. Due to space limitations, we focus in this manuscript on HCs design for Na-ion batteries, while the extension to other ion chemistries will be explored in future work.\nOur revision:\n1. Added detailed description.\np 9, line 7-10\nEven when the charging-discharging rate increased to 10 C, Dig-HC delivered 280 mAh g-1 and maintained 87.4% capacity retention after 5000 cycles, outperforming biochar (retained 62.4% after 4000 cycles) and Kuraray HC (short-circuited at 3000th) (Fig. 3g). Furthermore, when used as an anode material in lithium‑ion batteries, Dig‑HC delivers a markedly higher capacity (385 mAh g−1 at 0.1 A g-1) than commercially reported graphite52 (372 mAh g−1 at 0.1 A g-1). It also exhibits excellent rate capability, retaining approximately 141 mAh g−1 under a high current density of 1 A g-1 (Supplementary Fig. 12).\np 16, line 2-6\nSignificantly, the intelligent carbonization establishes a transferable paradigm for materials discovery. By leveraging transfer learning64 to freeze universal structure-property layers, the model can be rapidly adapted to novel multi-ion systems with minimal experimental data, enabling the efficient inverse design of bespoke materials for next-generation energy storage.\n2. Added data and figures.\nSupplementary Fig. 12 Performance of lithium-ion batteries. a, Initial charge–discharge profiles. b, Rate capability. c, Performance of Dig-HC with that of reported commercial graphite at 1 A g-1.\nComment #2. Currently, the input of the machine learning model only includes heating process parameters, without integrating the chemical information of biomass precursors (such as elemental composition and functional group distribution). How to construct a multi-source input fusion model that incorporates both the intrinsic properties of biomass and process parameters as inputs to achieve more universal structure-performance prediction?\nResponse: We thank the reviewer for this suggestion. We prioritized Step 2 (biochar-to-HCs via PJH) for modeling because the drastic chemical restructuring inherent in the full two-step carbonization effectively decouples initial precursor properties from the final electrochemical performance. In contrast, PJH transition maintains relative chemical stability, while the ultrafast PJH facilitate the rapid, high-throughput data generation essential for robust machine learning.\nOur rationale for prioritizing process parameters over precursor-specific chemical features (e.g., elemental composition, functional group distribution) stems from the profound physicochemical decoupling that occurs during the two-step synthesis (long-duration pyrolysis followed by ultrafast PJH) (Fig. R2).\nFigure R2. Production process of Dig-HC\nDestructive carbonization: Biomass precursors undergo drastic atomic rearrangement and functional group elimination during high-temperature treatment. As demonstrated in our work, the final electrochemical performance is dictated by the specific process-structure interaction (i.e., the graphitic domains and pore architectures formed during the PJH stage) rather than the initial chemical state of the biomass (Fig. R3a). This is corroborated by our previous study (Joule, 2025, 9, 101812), which showed that even for chemically pure small molecules like PTCDA, the XRD and FTIR signatures of the carbonized products differ markedly from their precursors (Fig. R3b, c), rendering the initial chemical features poor predictors of the final state. Consequently, constructing predictive models based directly on precursor characterization is both challenging and unreliable.\nOur data further show that different precursors can converge to nearly identical performance under optimized PJH conditions, whereas a single precursor can diverge substantially simply by varying the heating temperature (Fig. R3d-g) (Energy Storage Mater 2025, 80, 104367; ACS Nano, 2025, 19, 14829–14838). Thus, models relying solely on precursor chemistry would fail to capture the dominant role of the intelligent carbonization process.\n[Figure Redacted]\nBiomass diversity: To probe the feasibility of multi-source input fusion, we systematically investigated mixtures of cellulose, hemicellulose, and lignin—the fundamental building blocks of biomass (Nat. Rev. Chem. 2018, 2, 382–389)—across four compositional regimes (Table R1; Fig. R4). Dig-HCs were first synthesized via PJH, followed by XRD-based structure–performance prediction to identify optimal targets. These performance targets were used as inputs to the GPR model to inversely identify process windows. This integrated workflow successfully tuned compositions with distinctly different precursor chemistries to converge at a uniform performance level (~330 mAh g-1). These results suggest a promising pathway: by decomposing complex biomass into fundamental structural units and integrating these with process parameters, a multi-source input fusion model becomes feasible. We envision that such a framework will enable more universal structure–performance prediction across diverse biomass systems in future work.\nTable R1. Dig-HC samples derived from varying ratios of cellulose, hemicellulose, and lignin.\nSample cellulose hemicellulose lignin Capacity (mAh g-1)\nC1H2L7 10wt% 20wt% 70wt% 327\nC3H5L2 30wt% 50wt% 20wt% 330\nC5H1L4 50wt% 10wt% 40wt% 329\nC7H2L1 70wt% 20wt% 10wt% 339\nFigure R4. a, XRD patterns of four samples with different composition ratios. b, Initial charge–discharge profiles. c, Consistency of electrochemical performance and structural parameters among four optimized precursor compositions.\nOur revision:\n1. Added detailed description.\np 15, line 26-27; p 16, line 1-6\nAs a result, our optimization strategy can consistently deliver consistent and high-capacity HCs stabilized at 340 mAh g-1, regardless of precursor origin (Fig. 5d, Supplementary Table 11).\nFurthermore, when substituting the input variables with the fundamental lignocellulosic ratios (cellulose, hemicellulose, and lignin), our intelligent carbonization strategy successfully converts these diverse compositions into performance-unified HC anodes (330 mAh g-1) through iterative optimization (Supplementary Table 12, Supplementary Fig. 32). Significantly, the intelligent carbonization establishes a transferable paradigm for materials discovery. By leveraging transfer learning64 to freeze universal structure-property layers, the model can be rapidly adapted to novel multi-ion systems with minimal experimental data, enabling the efficient inverse design of bespoke materials for next-generation energy storage.\np. 10, line. 11-16\nMoreover, the rapid, cost-effective, and excellent reproducible nature of XRD makes it uniquely suited for generating the large datasets necessary to train a robust ML model and later industrial adoption. Conversely, techniques like high-resolution transmission electron microscopy (HRTEM) are ill-suited for large-scale feedback due to their localized sampling, complex preparation, and high operational costs. Moreover, relying on precursor characterization is infeasible, as the substantial evolution in phase and functional groups during carbonization severs the direct link between the starting material’s properties and the final anode performance.\n2. Added data and figures.\nSupplementary Fig. 32 a, X-ray diffraction (XRD) patterns of four samples with different composition ratios. b, Initial charge–discharge profiles. c, Consistency of electrochemical performance and structural parameters among four optimized precursor compositions.\nComment #3. Regarding the interpretability of the machine learning model's prediction results, can tools such as SHAP (SHapley Additive exPlanations) or Partial Dependence Plots be used to quantify the contribution of each input feature (process parameters, structural parameters) to the prediction results, thereby providing more explicit physical guidance for experimental design?\nResponse: We thank the reviewer for the question. As illustrated in the SHAP summary plot (Fig. 4f, Page 14 in original manuscript), the PCF emerges as the primary positive driver for capacity (Fig. R5), followed by La and d002.\nFigure R5. The SHAP summary plot for different structure features.\nSHAP dependence plot: To further elucidate these contributions, we conducted additional analysis using SHAP dependence plots. The results (Fig. R6a, b) reveal that both PCF and La exert a strong positive monotonic influence on predicted capacity. Crucially, however, the influence of d002 is non-monotonic (Fig. R6c); it exhibits a positive contribution only within 0.37–0.39 nm, whereas values deviating from this optimal window yield negative SHAP values, indicating a detrimental effect on capacity. Feature interaction analyses reveal that optimal interlayer spacing (d approximately 0.37–0.39 nm) yields a positive capacity contribution only when coupled with a sufficiently high PCF (Fig. R6d). Conversely, a low PCF remains detrimental regardless of the crystallite size (La) (Fig. R6e, f). This confirms that the dramatic elevation in PCF is the critical driver for the capacity leap observed in Dig-HC. Unlike conventional carbonization, which expands La at the expense of interlayer collapse, the PJH process uniquely engineers a synergistic structure—simultaneously maximizing PCF and La while kinetically pinning d002 within the optimal window—to unlock superior sodium storage.\nFigure R6. The SHAP dependence plots for a, PCF, b, La, and c, d002; the SHAP Interaction Plots between d, PCF and d e, PCF and La f, La and d002.\nMean SHAP values of process parameters: Furthermore, our analysis of SHAP values for the PJH parameters reveals that synthesis temperature (0.23) and heating duration (0.21) exert comparable positive influences on capacity (Fig. R7). This finding indicates that both factors are critical drivers of performance, suggesting that future material development strategies should prioritize the synergistic optimization of both temperature and time to maximize electrochemical outcomes.\nFigure R7. SHAP values of process parameters (temperature and duration of the PJH process)\nOur revision:\n1. Added detailed description.\np 11, line 14-18\nIt also clarified the nuanced role of d002, whose positive impact at a localized sweet spot (0.37–0.38 nm), thus reconciling our findings with the broader literature14, 20, 47. SHAP dependence plots (Supplementary Fig. 19) shows PCF and La have strong positive monotonic effects on predicted capacity, while d002 contributes positively within a narrow 0.37–0.39 nm window. Feature interactions indicate that enlarging d002 simply is ineffective, high capacity also demands a large La, and a high PCF. The PJH process uniquely co-optimizes PCF and La while pinning d002 in the optimal range, enabling the superior sodium storage.\n2. Added data and figures.\nSupplementary Fig. 19. The SHAP dependence plots for a, PCF, b, La, and c, d002; the SHAP Interaction Plots between d, PCF and d e, PCF and La f, La and d002.\nComment #4. For the specific capacity prediction using the Gaussian Process Regression (GPR) model, what is its predictive stability under small-sample datasets? Is it necessary to introduce Bayesian optimization or ensemble learning strategies to further improve the model's predictive accuracy in the edge regions of the process parameter space?\nResponse: We thank the reviewer for the question.\nStability of GPR model: A primary driver for selecting the Gaussian Process Regression (GPR) model was its established robustness in small-sample regimes and, critically, its intrinsic capability to quantify prediction uncertainty. Our dataset is, by nature, limited, and the high fidelity achieved by the trained model (Fig. 2f, Page 7 in manuscript) confirms its stability under these conditions. We additionally report in Fig. R8 the model accuracy after one iteration. Even with new data incorporated, the R² on both the training and test sets remains greater than 0.9, showing the stability of GPR model.\nBayesian optimization: In our original manuscript, we implemented a Bayesian optimization framework by coupling the GPR model with an Expected Improvement (EI) acquisition function (Nature Methods, 2023, 20, 1379–1387). As shown in Fig. 2f, the model achieved high predictive accuracy.\nDetails of EI function: Our active learning loop was designed to identify the optimal performance within a minimal number of experimental iterations (in this case, only one iterations). The critical step is the selection of the “next-best” experimental point. To achieve this, we employed a Bayesian Optimization sampling strategy. Specifically, we used the Expected Improvement (EI) as the acquisition function to guide the selection. The primary advantage of the EI function is its inherent ability to optimally balance the trade-off between exploitation and exploration. The EI is calculated as follows:\nEI(x)=(μ(x)− f(x+)−ξ)Φ(Z)+σ(x)φ(Z)\nwhere, μ(x) and σ(x) are the predictive mean and predictive standard deviation, respectively, of the GPR model at pointx. f(x+) is the best value observed among all experiments conducted so far. ξ is a tuning parameter that governs the balance between exploitation and exploration, for which we adopted the recommended default value of 0.01. Z =(μ(x)− f(x+)−ξ)/σ(x). Φ() and φ() are the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) of the standard normal distribution, respectively.\nIn each iteration of the active learning loop, we select the process parametersx* =argmaxEI(x)\nthat maximize the EI value as the next point for experimental validation.\nFigure R8. Model accuracy: a, original; b, after one iteration.\nOur revision:\n1. Added detailed description.\np 7, line 4-6\nAfter one iteration, the final model’s R² remains above 0.9, showing the stability of GPR model (Supplementary Fig. 6). The whole parameter space of our model spanned pyrolysis and PJH carbonization, with predictions across 1,453 generated parameter combinations within this extensive matrix (Fig. 2h, Supplementary Fig. 7) facilitating later ML-guided optimization and intelligent manufacturing.\nSupplementary Information p 31, line 2-31\nSupplementary Note 2. Details of machine learning for GPR model.\nOur Gaussian Process Regression (GPR) model was constructed using a Radial Basis Function (RBF) kernel as the covariance function, a standard and robust choice for modeling smooth response surfaces. The specific kernel was set as kernel = 1.0 * RBF (length scale=1.0); The primary advantages of the RBF kernel are its versatility and smoothness. As a stationary kernel, it is highly effective at capturing the smooth, non-linear response surfaces characteristic of materials properties, such as the capacity in this work. Its non-parametric nature allows it to flexibly fit complex functional forms without requiring a priori assumptions about the underlying mathematical relationship.\nThe active learning method includes the following steps: data collection, feature engineering, machine learning model construction, next experimental points design, experimental test, and data feedback. The key point of active learning is to design the next experimental points according to the predicted value and prediction uncertainty of the machine learning model, and then iteratively optimize the next modeling by the feedback of experimental results until the model prediction meets the requirements.\nOur active learning loop was designed to identify the optimal performance within a minimal number of experimental iterations (in this case, only one iterations). The critical step is the selection of the “next-best” experimental point. To achieve this, we employed a Bayesian Optimization sampling strategy, which evaluates the utility or acquisition function based on the model’s predicted mean value and prediction uncertainty to design the next experimental points. Specifically, we used the Expected Improvement (EI) as the acquisition function to guide the selection, which considers not only the probability of improvement but also the expected magnitude of improvement, is the widely used as utility function. The EI is calculated as follows:\nEI(x)=(μ(x)− f(x+)−ξ)Φ(Z)+σ(x)φ(Z)\nwhere, μ(x) and σ(x) are the predictive mean and predictive standard deviation, respectively, of the GPR model at pointx. f(x+) is the best value observed among all experiments conducted so far. ξ is a tuning parameter that governs the balance between exploitation and exploration, for which we adopted the recommended default value of 0.01. Z =(μ(x)− f(x+)−ξ)/σ(x). Φ() and φ() are the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) of the standard normal distribution, respectively.\nIn each iteration of the active learning loop, we select the process parametersx* =argmaxEI(x)\nthat maximize the EI value as the next point for experimental validation.\nComment #5. Dig-HC exhibits excellent rate performance in both ester-based and ether-based electrolytes. What are the differences in the interaction mechanisms between the electrolyte solvation structure and the surface/pore structure of Dig-HC? Could the authors further clarify the interface matching rules between the electrolyte and the electrode with the aid of characterization techniques?\nResponse: We thank the reviewer for this insightful question. The enhanced rate capability of Dig-HC in ether-based electrolytes originates primarily from the distinct solvation structures and SEI chemistries of the two electrolyte systems.\nThe interaction mechanisms: In ester-based electrolytes (e.g., EC/DEC), according to the radial distribution function, the coordination number of Na+ with O atoms in EC/DEC electrolyte is 4.2 (Fig. R9a). The strongly solvated Na ions undergo rapid carbonate ring-opening reactions upon contact with the hard carbon surface. This process generates a thick, heterogeneous organic–inorganic SEI that tends to occlude closed pore entrances, thereby kinetically hindering the diffusion of ions into the pores and limiting capacity utilization at the low-voltage plateau. Conversely, in ether-based electrolytes (e.g., DME), the loosely coordinated Na ions (the coordination number of Na+ with O atoms is 3.2) facilitate a progressive and efficient de-solvation mechanism (Fig. R9b). This promotes the formation of a thin, uniform, and inorganic-rich SEI. Such an interface effectively preserves pore accessibility, enabling rapid ion transport and maximizing low-voltage capacity utilization (Angew Chem Int Ed Engl, 2025, 64, e202425507).\n[Figure Redacted]\nThe interface matching rules: Dig-HC exhibits excellent rate performance in both ester-based and ether-based electrolytes (Fig. R10a, b). To clarify the interface matching rules between the electrolyte and the electrode, we performed the cyclic voltammetry (CV) test (Fig. R10c). The ester electrolyte exhibits a sharp, intense reduction peak between 0.6 and 0.2 V, indicative of aggressive cyclic carbonate decomposition and the rapid growth of a resistive SEI layer, which correlates with higher initial irreversible capacity loss. In contrast, the diglyme system displays a broader, lower-intensity reduction feature, reflecting moderated interfacial reactivity.\nTogether, these results highlight the key interface-matching rule: rapid de-solvation process that promote thin, inorganic-rich SEI formation are optimal for maximizing the accessibility of closed pores and enabling fast-charging performance in Dig-HC. This further demonstrates that the Dig-HC, characterized by a higher degree of graphitic ordering, is intrinsically well-suited for ether-based systems known for their rapid de-solvation kinetics.\nFigure R10. Rate performance in a, ether system. b, ester system. c, CV curves in ester and ether electrolytes.\nOur revision:\n1. Added detailed description.\np 12, line 24-27\nSuch developed closed porosity is believed to facilitate Na cluster formation, contributing to the low-voltage plateau capacity and concurrently bolstering ICE. Meanwhile, the first-cycle CV curves further indicate that this structure is more compatible with ether-based electrolytes than with ester-based ones, exhibiting sharper and higher peak currents and fewer side reactions, which facilitate the formation of a superior solid electrolyte interphase (Supplementary Fig. 23).\n2. Added data and figures.\nSupplementary Fig. 9 a, Cyclic Voltammetry (CV) curves of Dig-HC recorded at 0.1 mV/s for the first three cycles. b, Rate performance for different HCs.\nSupplementary Fig. 23 Initial cycle cyclic voltammetry (CV) curves of Dig-HC in ester and ether electrolytes.\nComment #6. What are the specific differences in the XRD-characterized parameters (PCF, La and d002) between Dig-HC and biochar? How do these differences directly affect their sodium storage capacities?\nResponse: Thank you for this question. We provide a direct comparison of these parameters in original Figure 4g (Fig. R11). Relative to biochar, Dig-HC exhibits a substantially more developed in-plane microstructure: the PCF increases from 0.12 to 0.20, and La expands from 2.18 nm to 2.64 nm. These enlarged graphitic domains supply a greater number of energetically favorable sites for Na⁺ adsorption and subsequent pore filling. Importantly, despite the ultrafast thermal shock, the interlayer spacing remains pinned within the optimal range for Na⁺ intercalation (0.37 nm in Dig-HC vs. 0.38 nm in biochar), ensuring efficient insertion kinetics.\nFigure R11. Changes in structural parameters for biochar and Dig-HC of microcrystalline structure.\nIn summary, while an expanded d002 provides the structural prerequisite for Na⁺ intercalation, the dominant performance enhancement arises from the PJH-induced amplification of in-plane ordering (higher PCF and La) combined with the formation of expanded closed pores (Fig. R11). This optimized microstructure markedly accelerates Na⁺ transport, raising the 10 C rate capacity from 180 to 280 mAh g⁻¹ and increasing the low-voltage plateau capacity (<0.1 V) from 37.77 to 234.87 mAh g⁻¹ (Fig. R12a, b).\nFigure R12. a, Rate performance. b, The proportions of the two stages in the second discharge curve: plateau (<0.1 V), and slope (>0.1 V).\nOur revision:\n1. Added detailed description.\np 11, line 23-24\nComparative analysis (Fig. 4g) showed Dig-HC possessed an increased PCF of 0.2 and a larger La of 2.64 nm relative to biochar, signifying a more ordered in-plane structure with larger graphitic domains.\nComment #7. XRD-derived PCF, Raman-derived I_D/I_G ratio, and XPS-measured C=C bond proportion all reflect the ordering degree of materials. What are the advantages and limitations of these three characterization techniques in quantitatively describing the graphitization degree of hard carbon, respectively? How to establish the quantitative conversion relationship between them?\nResponse: Thank you for your insightful questions. While XRD, Raman, and XPS all probe the degree of graphitic ordering, they operate at fundamentally different physical scales and sensitivities. It is a big challenge to establish the quantitative conversion relationship between them. The specific advantages and limitations are as follows.\n1. XRD (PCF): It serves as a bulk characterization technique that provides statistically averaged structural information over a large sample volume (mm3 scale), mitigating bias from local heterogeneity (Energy & Environmental Science, 2024, 17, 8189-8197). Crucially, the PCF is a mesoscopic morphological descriptor. It captures the relative dominance of in-plane ordering (La) versus c-axis stacking (Lc), effectively describing the unique “large sheet, thin stack” morphology of PJH-treated carbon. It is less sensitive to the chemical states of surface functional groups compared to XPS, which is not important to the sodium storage (Fig. R13a).\n2. Raman (ID/IG): Raman spectroscopy is exceptionally sensitive to short-range disorder and defects (e.g., edge sites, vacancies) via phonon vibration modes (μm scale). Furthermore, the ID/IG ratio often exhibits similarity in HCs (Energy & Environmental Science 2024, 17, 1387-1396), limiting its quantitative linearity for ML modeling (Fig. R13b).\n3. XPS (C=C %): XPS provides precise quantitative analysis of chemical bonding states (e.g., sp2 vs. sp3) and heteroatom content. It is strictly a surface-sensitive technique (probing depth < 10 nm) (Adv Mater, 2025, e11632). Since sodium storage is primarily a bulk phenomenon occurring in internal pores and layers, surface chemistry alone cannot fully predict the capacity (Fig. R13c).\nEstablishing a mathematical conversion between these metrics is scientifically challenging because they measure fundamentally different physical phenomena: long-range lattice diffraction (XRD) vs. short-range phonon vibration (Raman) vs. surface photoelectron emission (XPS). However, these metrics are qualitatively consistent and mutually corroborating (Fig. R13). The PJH treatment leads to a simultaneous increase in the PCF (indicating extended in-plane order), a higher proportion of C=C bonds (indicating defect healing), and a slight decrease in the ID/IG ratio (indicating reduced disorder).\nFigure R13. Changes in structural parameters for biochar and Dig-HC. a, XRD. b, Raman. c, XPS.\nOur revision:\n1. Added detailed description.\np 13, line 11-14\nAccording to the X-ray Photoelectron Spectroscopy (XPS) results (Supplementary Table 8), C 1s spectra for Dig-HC revealed a higher proportion of C=C bonds (~284.8 eV), while O 1s spectra showed decreased C=O content (~532.3 eV) (Supplementary Fig. 28). This latter observation signifies effective impurity removal and suggests an increased sp3-carbon proportion as well as a more ordered carbon structure, which is considered beneficial for Na storage62. These results are consistent with the XRD and Raman data, further demonstrating the important role of PCF parameters for the enhanced battery performance.\nComment #8. In the intelligent manufacturing process of Dig-HC, what roles do in-situ XRD, PJH, and machine learning play respectively in the \"process-structure-performance\" chain? Please briefly explain the synergistic mechanism of the three in combination with Fig. 5a.\nResponse: We thank the reviewer for this important question regarding the specific roles and data flow within our intelligent manufacturing system. As illustrated in Fig. R14, the synergy relies on a seamless data stream connecting rapid synthesis, structural digitization, and predictive optimization:\nFigure R14. The intelligent manufacturing workflow.\nStep1: High-throughput synthesis (PJH)\nPJH acts as the execution terminal for rapid material generation. It converts diverse precursors into hard carbons via a transient, sub-minute heating process, providing the physical foundation for high-throughput screening.\nStep2: Structural digitization (In-situ XRD)\nQuasi-in-situ XRD functions as the sensing module. It instantly characterizes the synthesized hard carbon, extracting high-dimensional structural features (e.g., PCF, La) to digitize the material state without offline delays.\nStep3: Performance prediction & structural recommendation (MLP Model)\nThe deployed MLP model serves as the precise predictor. It maps the XRD-derived features to electrochemical performance, accurately forecasting the capacity and identifying the optimal structural and property targets for the specific precursor being tested.\nStep4: Process optimization feedback (GPR Model)\nCrucially, the performance and structural targets identified by the MLP are fed back into the GPR model. The GPR model then performs inverse design to recommend the optimal process parameter window (T2, t2) required to achieve those targets.\nThis closed-loop workflow eliminates the need for cell assembly, enabling the rapid screening and process optimization of diverse biomass precursors in a fraction of the time required by conventional methods.\nOur revision:\n1. Added detailed description.\np 15, line 1-6\nIn this workflow, the ultrafast (<1 min) PJH platform performs high-throughput synthesis. Concurrently, in-situ XRD extracts key structural features (e.g., PCF, La, d002). Based on our pre-established process-structure-property model, the ML algorithm uses these features to predict battery’s performance, perform inverse design, and generate recommendations for optimal process parameters. These recommendations are immediately fed back to the PJH process, enabling precise and rapid tuning of the HC’s structural features to meet target performance.\n2. Added data and figures.\nSupplementary Fig. 28 The intelligent manufacturing workflow.\nComment #9. Regarding the convergence of structural parameters in Fig. 5d, Dig-HCs derived from cotton, peanut shells, and glucose exhibit structural convergence in PCF, La and d002. From the perspective of the stage evolution of \"precursor pyrolysis-graphitization\" during carbonization, what common mechanisms exist among the three in terms of graphite nucleation growth rate or other aspects during the PJH stage?\nResponse: We thank the reviewer for this insightful inquiry into the mechanism underlying structural convergence. We propose that the observed convergence of PCF, La, and d002 in Dig-HCs does not arise from an intrinsic, precursor-independent graphitization pathway. Instead, it is the direct consequence of the ML-guided inverse-design framework, which adaptively compensates for the distinct chemical compositions and graphitization kinetics of different biomass feedstocks.\nML-guided: From the perspective of the pyrolysis–graphitization stage, different biomasses possess inherently different molecular structures and activation energies, and conventional synthesis cannot unify their structural outcomes. In our workflow, however, the ML model tailors the thermodynamic input for each precursor, effectively overcoming these intrinsic kinetic disparities and steering all feedstocks toward the same high-performance structural optimum.\nCommon mechanisms: Mechanistically, the convergence is enabled by the unique heating dynamics of the PJH process. The ultrafast temperature ramp fractures the disordered graphitic stacks in the pre-pyrolyzed biochar (Lc decreases from 1.06 to 0.75 nm), while the subsequent ~20 s isothermal hold promotes lateral crystallite growth along the a-axis (La increases from 2.18 to 2.64 nm). The final rapid quench—from ~1800 °C to room temperature in <5 s (Fig. R15a-c)—induces curling and reorganization of short-range ordered domains, collapsing and coalescing the micropore network into larger pores (Fig. R15d-f).\nIn a word, the ML-driven process optimization and the dynamic microstructural reconstruction under PJH jointly enforce structural convergence across diverse precursor chemistries.\nFigure R15. a, The temperature profile of the PJH process. b, The XRD-derived graphitic crystallite parameters of biochar and Dig-HC. c, The SAXS data of biochar and Dig-HC. TEM images of the three PJH-treated materials d, peanut shells. e, cotton. f, glucose.\nOur revision:\n1. Added figures.\nSupplementary Fig. 31 TEM images of the three PJH-treated materials a, peanut shells. b, cotton. c, glucose.\nComment #10. We kindly ask the authors to check the English expressions in the manuscript. For instance, \"a increased PCF\" in Line 2 of Page 11 should be corrected to \"an increased PCF\" (since \"increased\" starts with a vowel sound, the indefinite article \"an\" is grammatically appropriate here).\nResponse: We sincerely thank the reviewer for this careful observation. We will correct this error in the revised manuscript and perform a thorough grammar and spelling check throughout the text to ensure overall linguistic accuracy.\nOur revision:\n1. Grammar or spelling correction.\np 4, line 1-2\n…posing a profound challenge of elucidating their structure-performance relationships.\np 9, line 1-2\nIt surpassed Kuraray HC, which delivered a capacity of 225.7 mAh g-1 before it short-circuited at the 17th cycle under identical conditions (Fig. 3f).\np 10, line 19-20\nSeven indices were chosen for subsequent analysis, including six physically meaningful features of…\nReviewer #2 (Remarks on code availability):\nYes. The code is well-organized and comes with a comprehensive README file that includes clear instructions for installation and execution. It serves as a valuable and usable resource for the research community.\nResponse: We sincerely appreciate the reviewer’s positive comments on the code organization and documentation.\nWe sincerely thank you for your constructive comments and careful evaluation of our work. We hope that the substantial revisions and new analyses provided in this response satisfactorily address all of your concerns.\nReviewer #3\nThe study titled \"Data-driven intelligent carbonization unifies diverse biomass into high-performance hard carbon anodes\" by Cui et al. presents an active learning-driven strategy to optimize capacity of biomass-derived hard carbons. This work is of significant value to the battery community as it provides a promising solution to scaling of cheap and widely available biomass-derived synthesis of hard carbon anodes. I do have a few comments which the authors should take care of before accepting it for publication (minor revision):\nResponse:\nWe sincerely thank the reviewer for their highly positive evaluation and for recognizing the significant value of our work to the battery community. We have carefully addressed your specific comments to further improve the quality and clarity of the manuscript. Please find our detailed, point-by-point responses below.\nComment #1. SHAP dependence plots for important features like PCF should also be plotted to check the trend of capacity as a function of these features. The authors should also make a comment on whether the trends are in line with expected behavior.\nResponse: We thank the reviewer for this highly valuable suggestion, which will significantly enhance the interpretability of our ML model. The reviewer is correct in pointing out that our current Fig. 4f presents a SHAP summary plot (Fig. R1), which primarily illustrates overall feature importance. As suggested, we will incorporate the SHAP dependence plots for PCF, La, and d002 into our revised manuscript. Furthermore, this result is consistent with the SHAP summary plot, which corroborates the critical importance of these features in determining capacity.\nFigure R1. The SHAP summary plot for different structure features.\nSHAP dependence analysis reveals distinct structure-property laws: both PCF (Fig. R2a) and La (Fig. R2b) exhibit strong positive monotonic correlations with capacity, whereas d002 contributes positively only within a specific sweet spot of ~0.37–0.39 nm (Fig. R2c). Crucially, interaction plots demonstrate that the benefits of an optimal d002 are contingent upon sufficiently high PCF and La values (Fig. R2e, f); conversely, a low PCF remains detrimental regardless of crystallite size (Fig. R2d). This underscores that the PJH-induced elevation in PCF is the primary driver for performance. Unlike conventional carbonization, which expands La at the expense of interlayer collapse, the PJH process uniquely engineers a synergistic structure—simultaneously maximizing PCF and La while kinetically pinning d002 within the optimal window—to unlock superior sodium storage.\nFigure R2. The SHAP dependence plots for a, PCF, b, La, and c, d002; the SHAP Interaction Plots between d, PCF and d e, PCF and La f, La and d002.\nOur revision:\n1. Added detailed description and reference.\np 11, line 14-18\nIt also clarified the nuanced role of d002, whose positive impact at a localized sweet spot (0.37–0.38 nm), thus reconciling our findings with the broader literature14, 20, 48. SHAP dependence plots (Supplementary Fig. 19) shows PCF and La have strong positive monotonic effects on predicted capacity, while d002 contributes positively within a narrow 0.37–0.39 nm window. Feature interactions indicate that enlarging d002 simply is ineffective, high capacity also demands a large La, and a high PCF. The PJH process uniquely co-optimizes PCF and La while pinning d002 in the optimal range, enabling the superior sodium storage.\n2.Added data and figures.\nSupplementary Fig. 19 The SHAP dependence plots for a, PCF, b, La, and c, d002; the SHAP Interaction Plots between d, PCF and d e, PCF and La f, La and d002.\nComment #2. I am a bit lost on the difference between GP-driven active learning and two other MLP developed for predicting specific capacity and structural parameters. It is not clearly explained in the draft why is there a need for other two MLPs.\nResponse: We sincerely apologize for the confusion caused by the unclear description in our original draft. It was a slip of the pen to imply the use of three completely disparate modeling frameworks. In reality, we utilized two fundamental types of machine learning models—Gaussian Process Regression (GPR) and Multi-Layer Perceptron (MLP)—to address distinct challenges within our process-structure-property research paradigm (Fig. R3).\nThe necessity for these specific models for different tasks is explained as follows:\nFigure R3. a, GPR model. b, MLP model.\n(1) GPR for process optimization: we chose GPR for the active learning loop because it is highly effective for small datasets and provides uncertainty estimates (Nature Methods, 2023, 20, 1379–1387) (essential for the Expected Improvement acquisition function), enabling us to rapidly identify optimal synthesis parameters with minimal experiments.\n(2) MLP for scientific understanding: we developed this model to decode the complex, non-linear relationships between purely structural descriptors and electrochemical performance. This model was crucial for performing SHAP analysis (Fig. 4f) to identify which structural features are the key drivers of capacity.\nAs illustrated in Fig. R4, both models are indispensable components of the optimization framework. Given that the theoretical performance limit varies intrinsically across different precursors, the MLP model is first employed to rapidly predict capacity and identify the optimal structural and performance window for a specific precursor, utilizing only XRD spectral data. These targets are subsequently fed into the GPR model, which inversely recommends the optimal set of process parameters to achieve them, thereby establishing a continuous, iterative optimization loop.\nFigure R4. The intelligent manufacturing workflow.\nOur revision:\n1. Corrected the model details.\np 20, line 9-14\nTo quantitatively map the synthesis-structure-property relationships of the hard carbon, we developed a suite of machine learning models. First, a Gaussian Process Regression (GPR) model was established to predict the final specific capacity directly from four heating process parameters (designated T1, t1, T2, and t2). In parallel, a multilayer perceptron (MLP), incorporating Dropout and L2 regularization and optimized via grid search, was trained to model the link between six key structural parameters and specific capacity.\n2. Added MLP model details in Supplementary information.\nSupplementary Fig. 14 The workflow of MLP model.\nComment #3. Can authors comment on whether any direct material structure-based features can be used instead of XRD-derived features which will limit the screening of biomass on a large scale?\nResponse: We appreciate this insightful and forward-looking question, yet relying on such “direct” features poses significant practical obstacles.\nLimitations of direct material features: Precursor-specific traits, such as elemental composition or functional group distribution, are largely decoupled from the final electrochemical performance due to the profound structural reconstruction induced by high-temperature carbonization. As demonstrated in our work, the final performance is dictated by the specific process-structure interaction (i.e., the graphitic domains and pore structures formed during PJH) rather than the initial state of the biomass (Fig. R5a). Our previous work (Joule 2025, 9, 101812) demonstrated that, even for pure small-molecule compounds such as PTCDA, the XRD and FTIR spectra of the carbonized products differ markedly from those of their precursors (Fig. R5b-c). Different precursors can yield unified performance under optimized conditions, while the same precursor can yield vastly different results under different temperatures (Fig. R5d-g) (Energy Storage Materials 2025, 80, 104367) (ACS Nano, 2025, 19, 14829-14838). Consequently, constructing predictive models based directly on material characterization features is challenging and likely to produce inaccurate results.\n[Figure Redacted]\nAdvantages of XRD-derived features in large scale: Similarly, direct physical attributes of the resulting Dig-HCs either lack predictive power (e.g., color, density) or require time-intensive characterization incompatible with rapid screening (e.g., pore size distribution and atomic-scale images). Such features are fundamentally impractical for large-scale screening or the in-situ feedback loop shown in Fig. R6. In this context, XRD-derived descriptors emerge as the optimal solution, offering a robust, physically meaningful correlation with capacity while enabling the high-speed data acquisition essential for large-scale manufacturing (Fig. R7a). This is attributed to its ability to precisely characterize the microstructure of Dig-HC, coupled with a rapid workflow that spans less than 10 minutes from data acquisition to analysis, which can provide adequate data for ML (Fig. R7b).\nFigure R6. Intelligent manufacturing workflow for Dig-HC.\nFigure R7. a, Schematic illustrating the computation and physical meaning of the structural features of HC derived from XRD patterns. b, Enriched parameter space of XRD-derived features.\nTo systematically evaluate the feasibility of mixed-feedstock processing, we formulated precursors by blending cellulose, hemicellulose, and lignin in three distinct ratios (Table R1), guided by our ML framework. Samples are denoted as CxHyLz, where x, y, and z represent the respective component fractions in units of 10 wt% (e.g., C1H2L7 = 10 wt% cellulose, 20 wt% hemicellulose, 70 wt% lignin). Using rapid PJH synthesis, we generated a series of HCs spanning diverse structures (Fig. R8). The MLP model was applied to predict capacity and identify, for a given compositional class, precursor formulations and structural attributes that maximize performance. These predicted optima were then passed to a GPR model to efficiently locate the corresponding processing window. As a result, precursor mixtures with similar component ratios could be tuned to yield nearly identical electrochemical performance (~330 mAh g⁻¹). XRD analysis further confirmed that the key structural descriptors of the optimized samples—PCF, La, and d002—were closely aligned.\nThese results further validate the feasibility of employing XRD-derived features rather than direct structural characterization. Moreover, they demonstrate that this methodology enables the rapid optimization of diverse precursor inputs under large-scale conditions with minimal constraints.\nTable R1. Dig-HC samples derived from varying ratios of cellulose, hemicellulose, and lignin.\nSample cellulose hemicellulose lignin\nC1H2L7 10wt% 20wt% 70wt%\nC3H5L2 30wt% 50wt% 20wt%\nC5H1L4 50wt% 10wt% 40wt%\nC7H2L1 70wt% 20wt% 10wt%\nFigure R8. a, X-ray diffraction (XRD) patterns of four samples with different composition ratios. b, Initial charge–discharge profiles. c, Consistency of electrochemical performance and structural parameters among four optimized precursor compositions.\nOur revision:\n1. Added detailed description.\np 10, line 11-16\nMoreover, the rapid, cost-effective, and excellent reproducible nature of XRD makes it uniquely suited for generating the large datasets necessary to train a robust ML model and later industrial adoption. Conversely, techniques like high-resolution transmission electron microscopy (HRTEM) are ill-suited for large-scale feedback due to their localized sampling, complex preparation, and high operational costs. Moreover, relying on precursor characterization is infeasible, as the substantial evolution in phase and functional groups during carbonization severs the direct link between the starting material’s properties and the final anode performance.\nComment #4. Details of the active learning framework is also missing, for example, which covariance kernel was used, how many experiment feedback-active learning iterations were carried in this study, etc.\nResponse: We thank the reviewer for requesting these important model details. Our Gaussian Process Regression (GPR) model was constructed using a Radial Basis Function (RBF) kernel as the covariance function, a standard and robust choice for modeling smooth response surfaces (Sci. Technol. Adv. Mater 2023, 24, 2). The specific kernel was set as kernel = 1.0 * RBF (length scale=1.0); The primary advantages of the RBF kernel are its versatility and smoothness. As a stationary kernel, it is highly effective at capturing the smooth, non-linear response surfaces characteristic of materials properties, such as the capacity in this work. Its non-parametric nature allows it to flexibly fit complex functional forms without requiring a priori assumptions about the underlying mathematical relationship. These characteristics, combined with its ability to provide reliable uncertainty quantification, make the RBF kernel the ideal choice for Bayesian Optimization and the active learning loop guided by our acquisition function.\nThe active learning method includes the following steps: data collection, feature engineering, machine learning model construction, next experimental points design, experimental test, and data feedback. The key point of active learning is to design the next experimental points according to the predicted value and prediction uncertainty of the machine learning model, and then iteratively optimize the next modeling by the feedback of experimental results until the model prediction meets the requirements.\nOur active learning loop was designed to identify the optimal performance within a minimal number of experimental iterations (in this case, only one iterations). The critical step is the selection of the “next-best” experimental point. To achieve this, we employed a Bayesian Optimization sampling strategy, which evaluates the utility or acquisition function based on the model’s predicted mean value and prediction uncertainty to design the next experimental points. Specifically, we used the Expected Improvement (EI) as the acquisition function to guide the selection, which considers not only the probability of improvement but also the expected magnitude of improvement, is the widely used as utility function. The EI is calculated as follows:\nEI(x)=(μ(x)− f(x+)−ξ)Φ(Z)+σ(x)φ(Z)\nwhere, μ(x) and σ(x) are the predictive mean and predictive standard deviation, respectively, of the GPR model at pointx. f(x+) is the best value observed among all experiments conducted so far. ξ is a tuning parameter that governs the balance between exploitation and exploration, for which we adopted the recommended default value of 0.01. Z =(μ(x)− f(x+)−ξ)/σ(x). Φ() and φ() are the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) of the standard normal distribution, respectively.\nIn each iteration, we select the process parametersx* =argmaxEI(x) that maximize the EI value as the next point for experimental validation.\nOur revision:\n1. Added detailed description in Supplementary Information.\nSupplementary Information p 31, line 2-31\nDetails of machine learning for GPR model.\nOur Gaussian Process Regression (GPR) model was constructed using a Radial Basis Function (RBF) kernel as the covariance function, a standard and robust choice for modeling smooth response surfaces. The specific kernel was set as kernel = 1.0 * RBF (length scale=1.0); The primary advantages of the RBF kernel are its versatility and smoothness. As a stationary kernel, it is highly effective at capturing the smooth, non-linear response surfaces characteristic of materials properties, such as the capacity in this work. Its non-parametric nature allows it to flexibly fit complex functional forms without requiring a priori assumptions about the underlying mathematical relationship. These characteristics, combined with its ability to provide reliable uncertainty quantification, make the RBF kernel the ideal choice for Bayesian Optimization and the active learning loop guided by our acquisition function.\nThe active learning method includes the following steps: data collection, feature engineering, machine learning model construction, next experimental points design, experimental test, and data feedback. The key point of active learning is to design the next experimental points according to the predicted value and prediction uncertainty of the machine learning model, and then iteratively optimize the next modeling by the feedback of experimental results until the model prediction meets the requirements.\nOur active learning loop was designed to identify the optimal performance within a minimal number of experimental iterations (in this case, only one iterations). The critical step is the selection of the “next-best” experimental point. To achieve this, we employed a Bayesian Optimization sampling strategy, which evaluates the utility or acquisition function based on the model’s predicted mean value and prediction uncertainty to design the next experimental points. Specifically, we used the Expected Improvement (EI) as the acquisition function to guide the selection, which considers not only the probability of improvement but also the expected magnitude of improvement, is the widely used as utility function. The EI is calculated as follows:\nEI(x)=(μ(x)− f(x+)−ξ)Φ(Z)+σ(x)φ(Z)\nwhere, μ(x) and σ(x) are the predictive mean and predictive standard deviation, respectively, of the GPR model at pointx. f(x+) is the best value observed among all experiments conducted so far. ξ is a tuning parameter that governs the balance between exploitation and exploration, for which we adopted the recommended default value of 0.01. Z =(μ(x)− f(x+)−ξ)/σ(x). Φ() and φ() are the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) of the standard normal distribution, respectively.\nIn each iteration of the active learning loop, we select the process parametersx* =argmaxEI(x)\nthat maximize the EI value as the next point for experimental validation.\nReviewer #3 (Remarks on code availability):\nThanks for sharing all the data and the codes, it will be a valuable resource for the community. However, there is no README file available. Please also make available the README file containing all the relevant information about how to run the codes. I also noticed that the comments and descriptions in the python script files are written in Chinese language which will make it difficult for the international readers to follow, so please convert them to English.\nResponse: We thank the reviewer for the constructive suggestions. We have now included a comprehensive README file with detailed execution instructions and have translated all comments in the Python scripts from Chinese to English. The updated code and data have been uploaded to Code Ocean for better accessibility and reproducibility, and can be accessed via the following link:\nhttps://doi.org/10.24433/CO.8253729.v3\nWe sincerely thank you for your constructive comments and careful evaluation of our work. We hope that the substantial revisions and new analyses provided in this response satisfactorily address all of your concerns.\nResponse to referees\nReviewer #1 (Remarks to the Author):\nThe authors have addressed the comments and this manuscript can be accepted now.\nOur response：We thank the reviewer for the positive evaluation and for confirming that all comments have been satisfactorily addressed.\nReviewer #2 (Remarks to the Author):\nThe author's response has basically resolved the issues raised previously. I think this paper can be accepted.\nOur response：We sincerely thank the reviewer for recognizing that the previous issues have been resolved and for supporting the acceptance of our work.\nReviewer #3 (Remarks to the Author):\nAll my comments have been satisfactorily taken care of. I recommend it for publication in Nature Communications.\nOur response：We are grateful to the reviewer for the positive assessment.\nReviewer #3 (Remarks on code availability): The authors have made relevant changes in the codebase as I had requested.\nOur response：We thank the reviewer for reviewing our code."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed the comments and this manuscript can be accepted now.", "reviewer_2": "The author's response has basically resolved the issues raised previously. I think this paper can be accepted.", "reviewer_3": "All my comments have been satisfactorily taken care of. I recommend it for publication in Nature Communications."}, "author_response": "Our response：We thank the reviewer for the positive evaluation and for confirming that all comments have been satisfactorily addressed.\nOur response：We sincerely thank the reviewer for recognizing that the previous issues have been resolved and for supporting the acceptance of our work.\nOur response：We are grateful to the reviewer for the positive assessment.\nOur response：We thank the reviewer for reviewing our code."}]

Decision letter