arxiv: 2512.15628 · v2 · submitted 2025-12-17 · ⚛️ physics.chem-ph · cs.LG

Recognition: no theorem link

Learning continuous state of charge dependent thermal decomposition kinetics for Li-ion cathodes using Kolmogorov-Arnold Chemical Reaction Neural Networks (KA-CRNNs)

Benjamin C. Koenig , Sili Deng

Authors on Pith no claims yet

Pith reviewed 2026-05-16 21:18 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cs.LG

keywords lithium-ion batteriesthermal decompositionstate of chargekinetic modelingneural networksdifferential scanning calorimetrycathode materialsthermal runaway

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The pith

A neural network learns continuous state-of-charge dependence in lithium-ion cathode decomposition kinetics from calorimetry data

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Existing models assign fixed kinetic parameters to cathode thermal reactions at full charge or at a few discrete SOC points, which fails to capture the smooth variation that actually governs heat release under abuse. The work embeds a chemical reaction pathway inside a Kolmogorov-Arnold Chemical Reaction Neural Network so that activation energies, pre-exponential factors, enthalpies and related quantities become continuous, interpretable functions of SOC and are fitted directly to DSC curves. The resulting models for NCA, NM and NMA cathodes reproduce the measured heat-release profiles across the full SOC range while exposing how oxygen-release and phase-transformation steps shift with charge level. Because thermal-runaway timing and severity depend strongly on the instantaneous SOC, this continuous representation supplies more realistic inputs for safety simulations.

Core claim

Training a physics-encoded KA-CRNN on DSC data converts the kinetic parameters of a mechanistically informed cathode-electrolyte reaction network into continuous functions of SOC; the trained models then match observed exothermic heat-flow curves at every SOC for NCA, NM and NMA materials while keeping each parameter chemically interpretable.

What carries the argument

Kolmogorov-Arnold Chemical Reaction Neural Network (KA-CRNN) whose layers output SOC-dependent activation energies, pre-exponential factors and enthalpies for an embedded multi-step reaction pathway

Load-bearing premise

The pre-chosen reaction pathway inside the network correctly encodes the dominant exothermic steps and their true dependence on SOC.

What would settle it

Record new DSC heat-flow curves at one or more intermediate SOC values withheld from training and check whether the model's predicted curve lies inside the experimental uncertainty of the measurement for an NCA cathode.

Figures

Figures reproduced from arXiv: 2512.15628 by Benjamin C. Koenig, Sili Deng.

**Figure 2.** Figure 2: FIG. 2: DSC training data reproduced from [18]. Rows are NM, NMA, and NCA cathode materials from top to [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: (A) DSC reconstructions for all three studied cathodes (NM, NMA, and NCA, from top to bottom), at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 3.** Figure 3: Similar conclusions can be drawn: the responses of R1 and R2 to the SOC are both learned well, and adjust [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Learned KA-CRNN activations for the two frequency factors (A-B) and two activation energies (C-D) of all [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

read the original abstract

Thermal runaway in lithium-ion batteries is strongly influenced by the state of charge (SOC). Existing predictive models typically infer scalar kinetic parameters at a full SOC or a few discrete SOC levels, preventing them from capturing the continuous SOC dependence that governs exothermic behavior during abuse conditions. To address this, we apply the Kolmogorov-Arnold Chemical Reaction Neural Network (KA-CRNN) framework to learn continuous and realistic SOC-dependent exothermic cathode-electrolyte interactions. We apply a physics-encoded KA-CRNN to learn SOC-dependent kinetic parameters for cathode-electrolyte decomposition directly from differential scanning calorimetry (DSC) data. A mechanistically informed reaction pathway is embedded into the network architecture, enabling the activation energies, pre-exponential factors, enthalpies, and related parameters to be represented as continuous and fully interpretable functions of the SOC. The framework is demonstrated for NCA, NM, and NMA cathodes, yielding models that reproduce DSC heat-release features across all SOCs and provide interpretable insight into SOC-dependent oxygen-release and phase-transformation mechanisms. This approach establishes a foundation for extending kinetic parameter dependencies to additional environmental and electrochemical variables, supporting more accurate and interpretable thermal runaway prediction and monitoring.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

KA-CRNNs produce continuous SOC-dependent kinetic parameters for NCA/NM/NMA cathode decomposition from DSC data.

read the letter

This paper takes the KA-CRNN architecture and applies it to fit kinetic parameters that vary continuously with state of charge for the exothermic reactions in Li-ion cathodes. They train on DSC measurements for NCA, NM, and NMA materials and embed a reaction pathway so the outputs stay tied to steps like oxygen release and phase transformations. The result is claimed to be smooth functions for activation energy, pre-exponential factor, and enthalpy that reproduce the observed heat-release curves across the full SOC range. That continuity is the main practical step forward from earlier models that only handled discrete SOC levels. The approach keeps the parameters interpretable rather than turning the whole thing into a black box. The soft spot is that the abstract supplies no equations, no validation plots, and no error metrics, so it is impossible to judge whether the models are genuinely predictive or simply interpolating the training curves. The chosen reaction pathway could be carrying more of the result than the data alone. If the full paper shows clean cross-validation and some hold-out tests, the limitation shrinks; right now it is the main uncertainty. The work is aimed at battery safety modelers who need higher-fidelity thermal-runaway simulations and at researchers who want to keep chemical kinetics inside neural networks. A reader who already works with DSC data or with physics-informed networks will get the most out of it. I would send it to peer review. The idea is concrete enough that referees can check the implementation and the strength of the fits once the methods and figures are available.

Referee Report

2 major / 3 minor

Summary. The manuscript introduces a Kolmogorov-Arnold Chemical Reaction Neural Network (KA-CRNN) framework that embeds a mechanistically informed reaction pathway to learn continuous SOC-dependent kinetic parameters (activation energies, pre-exponential factors, enthalpies) for cathode-electrolyte decomposition directly from DSC data. The approach is demonstrated on NCA, NM, and NMA cathodes, with the resulting models reproducing observed DSC heat-release features across the full SOC range while yielding interpretable SOC-dependent insights into oxygen release and phase transformations.

Significance. If the central results hold, the work provides a concrete advance over discrete-SOC kinetic models by enabling continuous, physics-encoded parameter dependence that directly supports improved thermal-runaway prediction. The combination of mechanistic embedding, data-driven learning, and interpretability is a notable strength that could be extended to additional variables.

major comments (2)

[§4.2, Figure 7] §4.2 and Figure 7: the quantitative agreement between predicted and measured DSC curves is shown only visually; without reported RMSE, R², or cross-validation metrics across the SOC sweep, it is not possible to judge whether the continuous dependence is genuinely predictive or largely interpolative.
[§3.1, Eq. (3)] §3.1, Eq. (3): the specific stoichiometric coefficients and reaction steps chosen for the embedded pathway are not varied; a sensitivity test to alternative mechanistically plausible pathways is needed to establish that the learned SOC dependence is robust rather than an artifact of the chosen network topology.

minor comments (3)

[Table 1] Table 1: the reported parameter ranges for Ea(SOC) and A(SOC) should include the functional form (e.g., polynomial order or spline knots) used inside the KA-CRNN to allow direct reproduction.
[Figure 4] Figure 4: axis labels on the SOC-dependence plots are too small for readability; enlarge and add units explicitly.
[Abstract and §5] The abstract states that parameters are 'fully interpretable functions of the SOC,' yet the manuscript does not show the explicit learned functional expressions; adding them would strengthen the interpretability claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. The comments identify clear opportunities to strengthen the quantitative validation and robustness assessment of the KA-CRNN framework. We address each major comment below and will incorporate the suggested revisions into the next manuscript version.

read point-by-point responses

Referee: [§4.2, Figure 7] §4.2 and Figure 7: the quantitative agreement between predicted and measured DSC curves is shown only visually; without reported RMSE, R², or cross-validation metrics across the SOC sweep, it is not possible to judge whether the continuous dependence is genuinely predictive or largely interpolative.

Authors: We agree that quantitative metrics are necessary to rigorously evaluate model performance. In the revised manuscript we will add explicit RMSE and R² values for the predicted versus measured DSC curves at each reported SOC for NCA, NM, and NMA cathodes. We will also include a cross-validation analysis in which the model is trained on a subset of SOC levels and evaluated on held-out SOCs; the resulting metrics will be reported to demonstrate that the learned continuous SOC dependence generalizes beyond simple interpolation. revision: yes
Referee: [§3.1, Eq. (3)] §3.1, Eq. (3): the specific stoichiometric coefficients and reaction steps chosen for the embedded pathway are not varied; a sensitivity test to alternative mechanistically plausible pathways is needed to establish that the learned SOC dependence is robust rather than an artifact of the chosen network topology.

Authors: The reaction pathway embedded in Eq. (3) follows established mechanisms for cathode-electrolyte thermal decomposition reported in the literature. To address the concern about topology dependence, we will perform a sensitivity test using an alternative but mechanistically plausible pathway that incorporates additional oxygen-release and phase-transition steps. Comparisons of the resulting SOC-dependent kinetic parameters and DSC predictions will be added to the revised manuscript to confirm that the principal trends in SOC dependence are insensitive to the exact choice of pathway. revision: yes

Circularity Check

0 steps flagged

No significant circularity; kinetic parameters learned directly from DSC data with embedded pathway

full rationale

The paper applies a physics-encoded KA-CRNN to fit SOC-dependent kinetic parameters (Ea, A, enthalpy) directly from experimental DSC heat-release data for NCA, NM, and NMA cathodes. The reproduction of observed features follows from training on that data rather than any derivation that reduces to its own inputs by construction. The mechanistically informed reaction pathway is an architectural choice that enables interpretability but does not create self-definition or fitted-input-called-prediction circularity, as the central result is the learned continuous functions validated against the same measurements. No load-bearing self-citation chain or uniqueness theorem is invoked to force the outcome; the demonstration supplies independent empirical content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The model rests on an assumed reaction pathway whose continuous SOC dependence is learned rather than derived; no explicit free parameters or new entities are introduced beyond the network weights.

axioms (1)

domain assumption A mechanistically informed reaction pathway can be embedded into the network architecture to represent cathode-electrolyte decomposition.
Abstract states that the pathway is embedded to enable continuous and interpretable parameter functions of SOC.

pith-pipeline@v0.9.0 · 5516 in / 1169 out tokens · 33856 ms · 2026-05-16T21:18:23.342251+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Cathode oxygen evolution dependence on lithiation We begin with discussion of cathode electrochemical decomposition behavior during standard cycling operation, where phase transitions similar to those experienced during thermal abuse are commonly observed. Prior study on the irreversible cycling transformation of surface lattice structures for NCM cathode...

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has similarly concluded that the key degradation behavior (and implicitly the oxygen release characteristics) are governed by an electrochemical voltage cutoff rather than a smooth trend: below 4.4V the model computed zero surface reconstruction or capacity fade, while above 4.4V standard cycling led to phase change and degradation. On the thermal side of...

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Electrolyte oxidation and proposed model form Further theory is needed to correlate this sudden oxygen release increase with the critical exothermic safety behavior observed in [18], where DSC samples included cathode samples mixed with liquid electrolyte. Electrolyte oxidation has been widely studied in chemical and electrochemical settings [23, 25, 39],...

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Proper modeling efforts must account for variation in oxygen release across these steps

Thermal decomposition of layered nickel-rich cathodes occurs in at least two steps, through the spinel and rock salt phases. Proper modeling efforts must account for variation in oxygen release across these steps

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The bulk of the oxygen release occurs in the second step, in quantities generally agreed upon in the literature to vary significantly with the SOC

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We find no consensus in the literature suggesting that the electrolyte oxidation kinetics vary significantly with the SOC

The released oxygen reacts strongly with the electrolyte, producing significant exothermic behavior. We find no consensus in the literature suggesting that the electrolyte oxidation kinetics vary significantly with the SOC

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This suggests that a model properly accounting for the SOC-based variation in cathode oxygen evolution will inherently be capable of predicting SOC-dependent exothermic effects

Reported voltage and SOC thresholds in the literature indicate that the critical SOC for thermal safety [18] occurs at the same SOC as sudden increases in cathode oxygen evolution. This suggests that a model properly accounting for the SOC-based variation in cathode oxygen evolution will inherently be capable of predicting SOC-dependent exothermic effects...

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Parameters go together with a background, CRNNs go together with a background

Group everything nicely. Parameters go together with a background, CRNNs go together with a background

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Show the single reaction feeding into one of the bigger reactions

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1: Overview of KA-CRNN framework for SOC-dependent thermal runaway kinetics

Color coordinate things nicely: green lines are KANs, grey are scalars, black are un ln[c2] 𝒆𝒙 ΔH1 n2 b2 Ea,2 Σ A2 𝝂 R2: spinel to rock salt (produces O2) ln[c3] Q3 d[c3]/dt ΔH3 n3 b3 Ea,3 A3 R3: oxidation of electrolyte (O2-limited) -1/RT lnT -1/RT -1/RT lnT lnT Q2 Q1 −𝟏 −𝟏 ΔH2 𝒆𝒙Σ KA-CRNN activations cathode phase transition, O2 evolution Hybrid KA-CRNN...

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