# Following reaction kinetics in multiphase systems using local descriptors from machine-learned interatomic potentials: Application to the solid electrolyte interphase

Agnieszka Warnicka, Gracie Chaney, Mathieu Salanne, Ambroise van Roekeghem

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## To cite this version:

Agnieszka Warnicka, Gracie Chaney, Mathieu Salanne, Ambroise van Roekeghem. Following reaction kinetics in multiphase systems using local descriptors from machine-learned interatomic potentials: Application to the solid electrolyte interphase. Materials today energy, 2026, 56, pp.102215. 10.1016/j.mtener.2026.102215. hal-05494860

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# Following reaction kinetics in multiphase systems using local descriptors from machine-learned interatomic potentials: application to the solid electrolyte interphase

Agnieszka Warnicka, Gracie Chaney, Mathieu Salanne and Ambroise van Roekeghem

## ABSTRACT

Machine-learning interatomic potentials have revolutionised atomistic simulations, yet the rich structural information embedded in their descriptors of the local atomic environments is still rarely exploited further for analysis purpose. In this article, we show that the descriptors from moment-tensor potentials can be reused, without additional feature engineering, to recognize atomic-scale phases that emerge during long molecular-dynamics trajectories using support vector machines. By converting machine learning descriptors into instantaneous structural fingerprints, our approach enables scalable, on-the-fly phase tracking in reactive multicomponent systems. We apply this classification technique to study phase decomposition and crystallization in large-scale simulations involving a Li-metal anode and a solid-state electrolyte Li₆PS₅Cl. This allows us to observe the beginning of segregation of the different degradation products after the first formation of a solid solution solid electrolyte interphase.

## 1. INTRODUCTION

All-Solid-State-Batteries (ASSB) are currently one of the most promising solutions for enhanced electricity storage. Using a solid electrolyte might enable the replacement of carbon anodes in Li-ion batteries by pure metallic lithium, thus leading to a substantial increase in the energy density of the devices. The main challenge lies in the formation of lithium dendrites upon cycling. These dendrites expand within the solid electrolyte, finally leading to the early failure of the battery. It is therefore necessary to control the interface between the anode and the electrolyte to enhance the performance and the safety of ASSBs. Similarly to the well-known case of liquid electrolyte-based lithium batteries, a solid-electrolyte interphase (SEI) forms at the anode surface in ASSBs that hinders conductivity and lithium transport during multiple charge-discharge cycles [1], [2], [3]. However, detailed experimental studies of the SEI composition and structures are challenging as the in situ analysis of these buried interfaces requires the development of complex instrumental setups [4].

For this purpose, MD simulations have become an essential tool, offering an atomistic description of structural evolutions across time and temperature scales. Recent *ab initio* and molecular dynamics (MD) studies have shown that this SEI often includes amorphous and crystalline decomposition products, which can disrupt ion pathways and degrade performance [5], [6], [7]. Accurately identifying the distinct phases is critical for linking atomic-scale structure to macroscopic phenomena such as conductivity, mechanical response, or phase stability. Traditionally, the analysis of local environments in MD data has relied on order parameters such as Steinhardt bond orientational parameters ($Q_i$, $W_i$) – based on a projection of the bonds onto spherical harmonics [8]; the local structure index (LSI), which quantifies the spread in distance of nearest-neighbour distances to identify structured versus disordered environments [9]; or translational order parameters, which quantify local symmetry, density, or atomic arrangements to distinguish between different structural motifs [10]. While they have proven their efficiency in many cases, these methods are often system-specific,
requiring manual tuning and predefined thresholds that limit their applicability to dynamically evolving materials [11]. Moreover, very often those hand-crafted parameters rely on the expert's knowledge to extract meaningful insights [12].

The growing influence of machine learning (ML) has recently transformed how phase identification is approached in atomistic simulations. The developments in ML-based descriptors design have been gradually replacing traditional order-parameter-based methods, which often lack the flexibility and scalability needed for modern atomistic simulations. Those deficiencies are especially evident in simulations involving thousands of atoms for tens of nanoseconds. Several methodologies have been developed to combine tailored features with supervised and unsupervised machine learning algorithms [13], [14]. An approach proposed by Spellings et al. relies on developed numerical fingerprints of crystal structures, inspired by bond orientational order diagrams, which are treated as an input for unsupervised learning (clustering methods) and supervised learning (artificial neural networks (NNs)) for classification of known structures to characterize self-assembled structures in simulations [15]. Similar methods consisting of Support Vector Machine (SVM) were applied beyond crystalline systems [16], [17]. Sarupria et al. used a deep learning architecture which identifies local structure directly from clouds of atomic coordinates, making it more adaptable [18]. In the above examples, the authors stress that the identification of non-crystalline phases and at interfaces is more delicate, and the design of the classification workflow was clearly separated from data production.

Recently, Machine Learning Interatomic Potentials (MLIPs) have emerged as a promising tool for skilled feature manufacturing. In 2006, Behler and Parinello proposed to represent the *ab initio* potential-energy surfaces with symmetry functions based on radial and angular properties of the local environments, which they used as input to a NN [19]. Since then, various types of MLIPs have been proposed, such as the artificial NNs-based interatomic potential [20], the Gaussian approximation potential [21] or the Moment Tensor Potential (MTP) [22]. Among them, MTP stands out for its balance between accuracy and computational efficiency [23]. Moreover, MTP has been successfully applied across diverse fields, including atomic layer deposition to develop precursor or calculation of stacking fault energies showcasing its remarkable abilities [24], [25], [26]. An important yet often underappreciated aspect of MLIPs is that they optimise descriptors for accurate energy and force predictions but also intermediateily encode rich structural information. In 2013, Geiger and Dellago used the same local description as Behler and Parrinello, but trained the NN to identify amorphous and crystalline structures instead [27]. This illustrates the tight connection between the problems of building MLIPs and of recognizing phases through the appropriate representation of atomic environments [28]. This suggests that MLIP descriptors can be used for identifying phases—without the need for separate, hand-crafted descriptors. This idea has been very recently tested by Sun et al [29]. They showed how using smooth overlap of atomic positions (SOAP) descriptors, derived from MLIPs, after a “denoising” step to account for thermal motion, reduces the workload and enables the identification of different ice phases from atomistic simulations.

In this study, we propose a complementary method, in which we combine MTPs with a simple and lightweight SVM classification scheme to streamline phase detection in a reactive multicomponent system. By encoding atomic positions, bond lengths, and angular relationships, MTPs provide a meaningful structural fingerprint that can be used to differentiate between phases with high reliability. [30] We showcase our approach by classifying the different degradation products in large-scale simulations of an interface between a Li-metal anode and a solid-state electrolyte Li₆PS₅Cl – a super ionic conductor with remarkable ionic conductivity at room temperature σ=1.33x10⁻³ S/cm [31]. This allows us to benchmark our results with previous literature but also to observe the beginning of crystalline phases segregation within the reduced electrolyte, thanks to longer simulations and larger
system scales. Our method enables automated, accurate, and scalable phase classification and offers a transferable framework not only for studying the kinetics of degradation in ASSBs, but also for the general analysis of large MD or Monte Carlo simulations including different phases.

## 2. METHODS

A sketch of the workflow is shown in Figure 1. It consists of MLIP training to obtain a force-field model and extract structural descriptors, followed by MD simulations using machine learning-derived forces. In the final stages, dimensionality reduction is applied to the ML descriptors based on principal component analysis (PCA) after normalization and then then SVM is applied for classification, to enable automated structural labelling and quantitative analysis of interfacial reactions and kinetics.

### 2.1 MLIP-MTP and MD

The MLIP-3 package was introduced in 2023 by Podryabinkin et al. [32]. In this software, the total energy of an atomic configuration, $E^{MTP}$, is the sum of the contributions $V^{MTP}$ from atomic neighborhoods $n_i$ for N atoms.

$$E^{MTP} = \sum_{i=1}^{N} V^{MTP}(n_i)$$

The function $V^{MTP}$ depends on local atomic neighborhoods $n_i = (z_i, z_j, r_{ij})$, where $z_i$ is the species of the central atom, $z_j$ is the species of a neighbouring atom, and $r_{ij}$ is the relative atomic position. Each $V^{MTP}$ is expressed as a linear combination of basis functions $B_\alpha$:

$$V^{MTP}(n_i) = \sum_{\alpha} \xi_{\alpha} B_{\alpha}(n_i)$$

The coefficients $\xi_\alpha$ are learnt during model training. To define a functional form of basis functions, a moment tensor descriptor is introduced:

$$M_{\mu,v}(n_i) = \sum_j f_{\mu}(|r_{ij}|, z_i, z_j) r_{ij} \otimes \dots \otimes r_{ij}$$

The descriptor $M_{\mu,v}(n_i)$ consists of two parts. The angular component $r_{ij}^{\otimes v}$ encodes information about the atomic neighborhood and is a tensor of order v. The radial part of the descriptor depends on a set of parameters $c = \{c_{\mu,z_i,z_j}^\beta\}$, which are determined during training using polynomial functions. The basis functions $B_\alpha$ are based on contractions of the $M_{\mu,v}$

The parameters $\xi_\alpha$ and the radial parameters collectively define a set of $\theta$ parameters that characterize the MTP. The MTP allows for calculations of forces and stresses of atoms based on analytical derivatives of the energy. Optimal $\theta$ parameters are determined during fitting of MTP, which refers to the process of optimizing the parameters of the MTP model to best reproduce reference quantum-mechanical data, typically obtained from Density Functional Theory (DFT). The number of descriptors increases with the complexity of MTP. Higher complexity increases the accuracy but it comes with the price of longer training and evaluation.

### 2.2 ACTIVE-LEARNING
Active learning is an efficient approach to improve machine learning models by iteratively selecting the most informative data points for training. During MD simulations, an extrapolation grade (y) is computed based on atomic configurations at each step to quantify how far a given atomic configuration deviates from the training set. If y surpasses a critical threshold, the configuration is flagged as unreliable, prompting the selection of representative structures for additional quantum-mechanical calculations. These new data points are incorporated into the training set, refining the potential and expanding its applicability. This iterative process continues until MD simulations can proceed without exceeding the extrapolation threshold, ensuring both accuracy and computational efficiency. By minimizing the number of costly first-principles calculations, this method significantly enhances the applicability of MTPs for long-time and large-scale simulation [33], [34].

The training set was built based on Golov and Carrasco's work [7] and used the same dataset as in Chaney *et al.* [5] consisting of 2787 configurations from AIMD. It was later expanded through active learning to 2798 configurations, using MD trajectories of 100 ps. DFT calculations used to train the MTP employed the generalized gradient approximation with Perdew-Burke-Ernzerhof (GGA-PBE) functional on 318-atom systems, a 400 eV plane-wave cutoff, and a Γ-centered 1×1×1 k-point mesh.

Molecular dynamics simulations were carried out in LAMMPS [35], using the trained MTP potential. The mathematical framework of the potential remained unchanged from previous versions and was applied in the same configuration mode used by Chaney *et al.* Simulations were run in the NPT ensemble at 300 K and under 1 bar pressure, regulated by a Nosé-Hoover thermostat and barostat [36]. A single velocity initialization seed was used with a 0.5 fs timestep.

## 2.3 SVM

SVMs are a type of supervised ML technique widely used in various fields, including text classification [37], materials science for crystallization prediction [38], and cyber security [39]. The technique was first introduced in 1995 by Vapnik [40] and has gained popularity due to its strong generalization ability [41]. SVM maps data into a high-dimensional space and separates it into distinct classes. For non-linear data, kernel functions can be applied. In this study, the radial basis function (RBF) kernel was used [42]. Hyperparameters of SVM were optimized during grid search.

One challenge with SVMs is their sensitivity to class imbalance, which can lead to misclassification since the algorithm tends to favour the majority class while overlooking the minority one [43]. To address this issue, two main approaches have been developed: the sampling-based method and the cost-sensitive method [44]. The former modifies the dataset to achieve a more balanced distribution, while the latter introduces error costs to different classes [45]. In this study, class balancing techniques were applied using Scikit-learn's grid search to assign different weights to different classes [46].

To build the features for the SVM, we concatenate the descriptors derived from MTP together with the chemical species for the atom of interest. Moreover, to improve the prediction of amorphous or crystalline phases in the system, atoms were grouped based on their closest neighbours to form new building blocks for the prediction set [47]. The analysis considered neighborhood sizes ranging from 4 to 20 atoms. Ultimately, 20 atoms were selected to form the building block, as cross-validation (CV) parameters confirmed this as the optimal configuration for the support vector machine analysis.

## 2.4 Data sets and classes
<figure><img src="image_3.png" /><figcaption>Figure 1 Sketch of the phase detection workflow. First, the MLIP is trained for the system of interest and a MD simulation is performed. In a second step, a phase classification is made based on the ML descriptors of the local environments using SVM, after optional dimensionality reduction by PCA.</figcaption></figure>

Starting from the Li/Li₆PS₅Cl interface model originally constructed by Chaney *et al.* [5], that consisted of 7956 atoms, a new system was built in which the electrolyte layer was extended from 57.8 Å to 101.5 Å in height to be able to observe the SEI formation process for a longer time before the full decomposition of the electrolyte. This model served as the foundation for developing a new method aimed at analysing the reaction kinetics, the formation of SEI and at the interface and the decomposition of the electrolyte. Once the optimization of the MLIP was completed, the resulting potential file was first used to output descriptors for the training datasets.

We have built two separate sets, one for phase classification, and the second one for crystalline/amorphous identification specifically. The first training set contained the reduced crystalline species expected from the decomposition of the electrolyte, including Li₂S, LiCl and Li₃P; together with Li-metal and the Li₆PS₅Cl electrolyte; and was generated using AIMD simulations of the individual bulk phases. As a result, we obtained 4 subsets for training – one for each species (Li, S, Cl, P), each subset having separate labels for specific phases. For example, as S atoms can exist in two phases, they are attributed two labels only by SVM – one for the electrolyte and one for Li₂S. These labels were used in the prediction process to first divide the system into different phases (electrolyte, electrode and degradation products).

The second training set was created also from the MLIP-extracted descriptors for crystalline and amorphous training sets, based on the dataset from Ref. [5] in which the authors used a custom tiling approach for the classification of amorphous and crystalline phases.

## 3. RESULTS

### 3.1 Data separability

Firstly, tests on a smaller model of 7956 atoms were done to confirm the reliability of the new method. The objective was to see if it could reproduce the results from Chaney *et al.*, such as the amount of reduced electrolyte as a function of time.
Figure 2 shows the results of Principal Component Analysis (PCA) [48], used to evaluate how well the bulk phases from the first training set (AIMD) for phases classification could be separated, and if the ML-MD data from the simulated interface could be easily identified to those phases. Despite an apparent overlap on the PCA plots, great separability between bulk phases was confirmed by SVM, with high five-fold CV accuracy scores for each species: Li:0.948, S:0.997, Cl:1.00, P:1.00.

<figure><img src="image_4.png" /><figcaption>Figure 2. Principal Component Analysis for all elements in their corresponding bulk phases (from AIMD) together with data from the ML-MD simulated interface (blue dots) to see how separable data is. Some snapshots of the Li-metal-Li<sub>6</sub>PS<sub>5</sub>Cl electrolyte interface are shown on the right for illustration (beginning and end of the simulation).</figcaption></figure>

On the other hand, for the second classification step, the distribution of crystalline and amorphous atoms showed poor separability and substantial overlap between the two categories (Figure 3, in which we visualise only two species out of four). SVM scores were unsatisfactory with high standard deviation. Consequently, we tried to apply another dimensionality reduction technique to the descriptors: the Uniform Manifold Approximation & Projection (UMAP) [49]. It has a significant advantage over PCA, as it is not linear and theoretically better suited for capturing complex patterns in high-dimensional data, since it better preserves the data's manifold geometry [49], [50]. However, in our case it failed to solve the separation problem, hence did not lead to any improvements in the prediction accuracy.
<figure><img src="image_5.png" /><figcaption>Figure 3. Comparison of the efficiency of PCA (left) and UMAP (right) methods for labelling Cl (top) and S (bottom) in crystalline and amorphous states for the training set.</figcaption></figure>

The SVM prediction analysis confirmed that the current model was insufficient for reliable full system interpretation (Table S1). Predictions made on reduced dimensionality revealed low recalls values – which are calculated as TP/(TP+FN) – for amorphous class with unacceptably high standard deviation scores. The test split on the training set exhibits most likely the main reason for the poor, unsatisfactory performance. In Figure 4, confusion matrices for all the species show that amorphous atoms are misclassified as crystalline atoms. They were calculated with a formula:

$$C_{norm}(i, j) = \frac{C(i, j)}{\sum_{k} C(i, k)}$$

where i is the actual class (the true label), j is the predicted class (the model's prediction), each true class i is divided by the total number of samples in that class. Higher values along the diagonal of the confusion matrix indicate better model performance, as they represent a larger proportion of correct predictions for each class – True Positive (TP) and True Negative (TN). For most species (except Li and Cl) the True Negative (TN) was almost equal to False Positive (FP). However, the prediction made solely on all descriptors, without prior dimensionality reduction, suggested potential for slightly improved performances (Table S1).
<figure><img src="image_6.png" /><figcaption>Figure 4. Confusion Matrices for all 4 species for a test split between crystalline and amorphous atoms done on PCA data.</figcaption></figure>

Other ML predictive models – k-nearest neighbours (KNN) and Random Forest (RF) – were checked to evaluate their ability to handle the problem of non-separable data. The obtained performance of RF was lower than SVM, strongly overestimating the crystalline phase except for the case of Li, while KNN displayed the weakest performance.

## 3.2 Longer-range descriptors including nearest neighbors

The results suggested that the descriptors of a single atom alone were insufficient to fully differentiate between crystalline and amorphous local environments, indicating the need for a more structure-sensitive approach to local environment analysis.

A set of nearest neighbours was introduced into the training set, determined using 3D Euclidean distance. The optimal number of neighbors was selected from 4, 6, 12, 16 and 20. Table S2 in supporting information presents how the accuracy, standard deviation and recall for amorphous atoms varied following SVM parameter tuning on the test split. Ultimately, 20 nearest neighbors were selected as this configuration provided high performance while keeping the standard deviation within a small range below 0.1.

The recall values for the test split were high, indicating the model's strong ability to correctly identify atomic states. Furthermore, when all features were used directly, with balanced classes (without applying PCA or normalization) in the 1st classification step, the CV-accuracy of phase prediction reached its maximum at 1.00 with a standard deviation of 0.0. This result highlights that dimensionality reduction may discard subtle but critical information needed to differentiate between
local environments. These findings validate the use of the full descriptor set for accurate phase labelling.

### 3.3 Kinetics and structure of SEI formation in Li|LiPSCl interface

As a benchmark, we display in Figure 5 the kinetics of formation of degradation products in amorphous and crystalline phases. The classification was performed using our ML descriptors-SVM technique previously described. The obtained pattern for SEI growth is similar to the one in Chaney et al [5]. The initial reaction between the Li metal anode and the electrolyte sets off the formation of an amorphous phase, followed by progressive crystallization of decomposition products in a 5Li₂S·Li₃P·LiCl solid solution with the Li₂S crystalline structure. In our simulations (Figure 5), SEI crystallinity increases with a square-root-of-time dependence at early stages (until 625 ps), characteristic of diffusion-limited processes [51]. At later times, the kinetics slow down, indicating that SEI crystallisation becomes increasingly hindered.

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /></figure>

Further analysis of the system required a verification of the noticed change in kinetics. The difference was noticeable around 1ns. Moreover, the aggregation of one of the species was noticeable by eye even before quantitative analysis while the simulation was getting closer to the end. A time dependent heat map was built using space binning of the atomic coordinates along the direction normal to the interface, to observe the formation of each phase over time and how the electrolyte is progressively reduced (Figure 6).

The Li-only heat-map shows how the electrode at both ends starts to vanish as Li⁰ is rapidly oxidized to Li⁺ by the electrolyte. The heat maps of Li₂S, Li₃P and LiCl represent the degraded products, which can be pure phases or solid solutions, amorphous or crystalline. LiCl seems to appear almost instantly and around 5 ns a narrow LiCl stripe appears at each interface. Noticeably it doesn't form a diffuse layer in the electrolyte but instead mostly follows the electrode surface and stays the closest species to Li-metal. Li₃P, however, forms just after the start of the reaction and progressively forms a wider layer. Shortly afterwards Li₂S takes shape exhibiting the same behaviour as Li₃P. Moreover, it seems that Li₂S and Li₃P form mixed layers between them as they appear to exist on same positions relative to z-axis (see also Fig. 7). The residual Li-metal film ceases to shrink, and electrolyte Li⁺ depletion visibly slows down (Fig. S1).

<figure><img src="image_10.png" /><figcaption>Figure 6. Time dependence of the atomic fraction of S, P and Cl species in different phases corresponding to degradation products (Li₃P, LiCl, Li₂S) and in Li-metal as a function of their height in the simulation.</figcaption></figure>

The crystalline/amorphous-resolved maps (Figure S3) confirm that every SEI crystalline phase first appears as a thin nucleus at the Li surface and then enlarges progressively from the amorphous
phase towards the middle of the system. As seen on Figures 6 and S3, Li₃P is the first to form a crystalline layer over the full system width, around the first 3 ns. From about 5 ns to 10 ns the Li₂S crystalline layer keeps spreading outward from the lithium surface. That means the interface is still well supplied with Li and sulphur species. Once that crystalline band is a few nanometers thick, transport through the existing Li₂S becomes sluggish and the thickness stabilizes. In case of Cl, Cl⁻ ions reach the interface and they stack up there, forming crystallized structures within a thin and very localized layer (Figure S3, 6).

Histograms with matching 3D visualizations of sampled MD snapshots were created to see which phase appears first at particular heights in the cell (Fig. 7). From both histograms and visualisations at 300 ps the aggregation of Cl becomes obvious, but what the plot for 15 ns highlights is that Chlorine atoms squeeze in between the electrode and Li₂S and Li₃P. It is possible that the relatively small number of Cl atoms in the system might limit the formation of a covering LiCl layer. As confirmed by the visualization, Li₃P is indeed the first one to form a layer over the full system width. Another important finding is the lack of sulphur in the histogram and visualization for 0.5 ps, although lithium reduced species are already detected. One reason could be that the SVM classification detects Li atoms in the 5Li₂S·Li₃P·LiCl solid solution (with a structure similar to Li₂S), while detecting S atoms in Li₂S requires a longer-range arrangement.

<figure><img src="image_11.png" /></figure>
<figure><img src="image_12.png" /><figcaption>Figure 7. Histograms and visualizations of Li, S, P and Cl in different phases (Li₃P, LiCl, Li₂S).</figcaption></figure>

## 4. CONCLUSIONS

We have presented a streamlined and scalable method for automated phase identification based on MLIP-derived descriptors and SVM classification and applied it to the Li/Li₆PS₅Cl system. These simulations give a rare, atom-by-atom view of how a complex solid-electrolyte interphase self-assembles on lithium metal. Exploiting longer and larger scales allows us to observe the segregation and organization of the different bulk crystalline phases, beyond the first formation of amorphous and crystalline solid solutions already pointed out by previous works. 15 ns after the beginning of the reaction, we find that LiCl starts to aggregate between Li-metal and a mixed Li₂S/Li₃P thick layer. At this stage, the SEI thickness is already around 5 nms but still continues to grow with logarithmic speed. This approach to analyze molecular dynamics data is generalizable to other systems and offers a practical alternative to hand-crafted structural analysis in atomistic simulations.

## 5. Author information

Agnieszka Warnicka – Université Grenoble Alpes, CEA, LITEN, Grenoble 38054, France

Gracie Chaney – Université Grenoble Alpes, CEA, LITEN, Grenoble 38054, France and Laboratoire de Chimie Théorique, Sorbonne Université, Paris, France

Mathieu Salanne – Physicochimie des Électrolytes et Nanosystèmes Interenciaux, Sorbonne Université, CNRS, F-75005 Paris, France and CNRS@CREATE, Singapore 138601, Singapore

Ambroise van Roekeghem – Université Grenoble Alpes, CEA, LITEN, Grenoble 38054, France

## 6. Acknowledgements

This project was initiated by Natalio Mingo, who sadly passed away before its completion. We thank Andrey Golov and Javier Carrasco for useful discussions and the dataset analysis from Ref. [5]. Mathieu
Salanne and Ambroise van Roekeghem acknowledge support from France 2030 through the project ANR-22-PEBA-0002.

## 7. Authors Contributions

A.W. developed the methodology, performed the data analysis and wrote the original draft. G.C. developed the datasets. M.S. and A.V.R. supervised the work. All authors edited and reviewed the manuscript.

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