Physics-Enhanced Deep Learning for Proactive Thermal Runaway Forecasting in Li-Ion Batteries

Abdul Malik; Jie Li; Muhammad Zunair Zamir; Saeed Mian Qaisar; Salman Khan; Syed Sajid Ullah

arxiv: 2604.20175 · v2 · submitted 2026-04-22 · 💻 cs.LG · cs.AI

Physics-Enhanced Deep Learning for Proactive Thermal Runaway Forecasting in Li-Ion Batteries

Salman Khan , Muhammad Zunair Zamir , Syed Sajid Ullah , Jie Li , Abdul Malik , Saeed Mian Qaisar This is my paper

Pith reviewed 2026-05-12 03:42 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords physics-informed LSTMlithium-ion batterythermal runaway predictionheat transfer equationsdeep learning for batteriestemperature forecastingphysical constraints in neural networks

0 comments

The pith

Adding heat transfer equations to LSTM training cuts battery temperature forecast errors by over 80 percent while enforcing physical consistency.

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

The paper shows how to embed the governing heat transfer equations into a standard LSTM model so that predictions of lithium-ion battery temperature respect thermodynamic rules. A physics-based term added to the loss function penalizes violations of thermal diffusion during training on sequences of voltage, current, charge state, stress, and surface temperature. This hybrid PI-LSTM produces forecasts that stay within physical bounds and generalizes across thirteen separate battery datasets. The result matters for real-time safety systems because early, reliable detection of overheating can prevent thermal runaway without relying on slow standalone physics simulations.

Core claim

The PI-LSTM framework integrates governing heat transfer equations directly into the deep learning architecture through a physics-based regularization term in the loss function. The model leverages multi-feature input sequences, including state of charge, voltage, current, mechanical stress, and surface temperature, to forecast battery temperature evolution while enforcing thermal diffusion constraints. On thirteen lithium-ion battery datasets the approach yields an 81.9 percent reduction in RMSE and an 81.3 percent reduction in MAE relative to a plain LSTM, eliminates non-physical temperature oscillations, and improves generalization across operating conditions.

What carries the argument

The physics-based regularization term added to the LSTM loss function that enforces thermal diffusion constraints during training.

If this is right

The model produces temperature forecasts that remain physically consistent and free of non-physical oscillations across diverse conditions.
It outperforms standard LSTM, CNN-LSTM, and MLP baselines on the same thirteen datasets by large margins in both RMSE and MAE.
The hybrid approach supports real-time thermal management without the computational cost of full physics simulations.
Physical constraints improve generalization, allowing the same trained model to handle varied operating regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same regularization strategy could be tested on other time-series forecasting tasks where known differential equations govern the underlying process.
Deploying the model in an online battery management system would require checking whether the physics term still prevents violations when input noise or sensor drift is present.
Extending the multi-feature inputs to include internal resistance or electrolyte concentration might further tighten the physical constraints.

Load-bearing premise

A single regularization weight derived from heat transfer equations can be added to the LSTM loss and will enforce physical consistency across varied battery conditions without new inconsistencies or per-dataset retuning.

What would settle it

Running the trained PI-LSTM on a fresh battery dataset with the regularization weight held fixed from the original training and finding either temperature predictions that violate diffusion laws or error reductions that shrink to match the plain LSTM baseline.

Figures

Figures reproduced from arXiv: 2604.20175 by Abdul Malik, Jie Li, Muhammad Zunair Zamir, Saeed Mian Qaisar, Salman Khan, Syed Sajid Ullah.

**Figure 1.** Figure 1: Experimental Setup for Thermal Runaway To simulate mechanical abuse conditions and observe the onset of thermal runaway (TR), a multi-instrument experimental setup was constructed. A mechanics testing machine ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 3.** Figure 3: Position-dependent thermal response of the cylindrical [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 2.** Figure 2: Position-dependent mechanical response of the cylin [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: Failure time and corresponding failure distance of the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: Thermal response of the cylindrical lithium-ion cell [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

**Figure 5.** Figure 5: Mechanical response of the cylindrical lithium-ion cell [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 8.** Figure 8: Influence of indenter geometry and state of charge on [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗

**Figure 9.** Figure 9: Thermal response of the cylindrical lithium-ion cell [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗

**Figure 11.** Figure 11: Structure of the LSTM network used for temperature [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗

**Figure 10.** Figure 10: Effect of state of charge (SOC) on the electrical [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗

**Figure 12.** Figure 12: Conceptual overview of the proposed PI-LSTM frame [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗

**Figure 13.** Figure 13: Workflow diagram of the PI-LSTM training and [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗

**Figure 14.** Figure 14: illustrates the temporal evolution of temperature and voltage during the short-circuit (SC) event. The plot highlights two distinct operational regions: the pre-SC phase (shaded in blue) where both temperature and voltage remain stable, and the post-SC phase (shaded in red) where a rapid thermal escalation is observed. The actual temperature rises sharply following the SC trigger and continues increasing … view at source ↗

**Figure 15.** Figure 15: Actual vs. PI-LSTM predicted temperature profile for [PITH_FULL_IMAGE:figures/full_fig_p010_15.png] view at source ↗

**Figure 16.** Figure 16: Comparison of prediction error metrics (MAE and [PITH_FULL_IMAGE:figures/full_fig_p010_16.png] view at source ↗

**Figure 17.** Figure 17: Electro-thermal-mechanical response of a lithium-ion [PITH_FULL_IMAGE:figures/full_fig_p011_17.png] view at source ↗

**Figure 19.** Figure 19: Post-test battery damage after thermal runaway ex [PITH_FULL_IMAGE:figures/full_fig_p011_19.png] view at source ↗

**Figure 18.** Figure 18: Temperature evolution across multiple battery tests [PITH_FULL_IMAGE:figures/full_fig_p011_18.png] view at source ↗

**Figure 20.** Figure 20: Thermal Runaway (TR) warning results V. CONCLUSION This study introduced a Physics-Informed Long Short-Term Memory (PI-LSTM) framework for predicting the thermal behavior of lithium-ion batteries under diverse mechanical abuse and operating conditions. By embedding the heat diffusion equation into the LSTM loss function, the proposed model enforces thermodynamic consistency while retaining the flexibilit… view at source ↗

read the original abstract

Accurate prediction of thermal runaway in lithium-ion batteries is essential for ensuring the safety, efficiency, and reliability of modern energy storage systems. Conventional data-driven approaches, such as Long Short-Term Memory (LSTM) networks, can capture complex temporal dependencies but often violate thermodynamic principles, resulting in physically inconsistent predictions. Conversely, physics-based thermal models provide interpretability but are computationally expensive and difficult to parameterize for real-time applications. To bridge this gap, this study proposes a Physics-Informed Long Short-Term Memory (PI-LSTM) framework that integrates governing heat transfer equations directly into the deep learning architecture through a physics-based regularization term in the loss function. The model leverages multi-feature input sequences, including state of charge, voltage, current, mechanical stress, and surface temperature, to forecast battery temperature evolution while enforcing thermal diffusion constraints. Extensive experiments conducted on thirteen lithium-ion battery datasets demonstrate that the proposed PI-LSTM achieves an 81.9% reduction in root mean square error (RMSE) and an 81.3% reduction in mean absolute error (MAE) compared to the standard LSTM baseline, while also outperforming CNN-LSTM and multilayer perceptron (MLP) models by wide margins. The inclusion of physical constraints enhances the model's generalization across diverse operating conditions and eliminates non-physical temperature oscillations. These results confirm that physics-informed deep learning offers a viable pathway toward interpretable, accurate, and real-time thermal management in next-generation battery systems.

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

This applies physics-informed regularization to LSTM for battery temperature forecasting and reports large error drops on 13 datasets, but the gains may depend on per-dataset tuning of the physics weight.

read the letter

The main takeaway is that the authors add a term from heat transfer equations to the LSTM loss to keep temperature predictions physically consistent and claim an 81.9% RMSE reduction versus plain LSTM across thirteen battery datasets. They also beat CNN-LSTM and MLP baselines by wide margins while using inputs like state of charge, voltage, current, stress, and surface temperature. The multi-dataset scale and the focus on eliminating non-physical oscillations are the parts that stand out as useful for safety work in batteries. The setup is a straightforward extension of existing physics-informed neural net ideas rather than a new framework, but the concrete application to proactive thermal runaway forecasting is new enough to be worth noting. What they do well is test the model on a reasonable number of real battery traces instead of one or two cases, which gives the results more weight than typical single-dataset papers. The claim that the physics term improves generalization across operating conditions is plausible if it holds. The soft spots are in the missing implementation details. The abstract does not explain how the heat equations are turned into a discrete loss term or how the regularization weight is chosen. If that weight was tuned separately for each dataset, the big percentage improvements could be an artifact of hyperparameter search rather than robust enforcement of thermal constraints. No ablations isolating the physics contribution, no error bars, and no statistical tests are mentioned, so it is hard to judge how much the physics term is actually doing. This paper is for researchers working on battery management systems who want ML models that stay within basic thermodynamic bounds. A reader already familiar with PINNs would get value from the dataset collection and the specific multi-feature LSTM setup, though they would still need the code or more methods to reproduce or extend it. It deserves a serious referee because the experiments are on a decent scale and the safety application is concrete. Referees can ask for the exact discretization, fixed versus per-dataset lambda, and ablations to see whether the physics constraint is load-bearing. I would send it to review rather than desk reject.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a Physics-Informed LSTM (PI-LSTM) that augments the standard LSTM loss with a regularization term derived from governing heat transfer equations. Multi-feature sequences (SOC, voltage, current, mechanical stress, surface temperature) are used to forecast battery temperature evolution and thermal runaway. Experiments on thirteen Li-ion battery datasets report an 81.9% RMSE reduction and 81.3% MAE reduction versus a baseline LSTM, with additional gains over CNN-LSTM and MLP models, plus elimination of non-physical oscillations and improved generalization.

Significance. If the central performance claims are robust to the choice of regularization weight, the work would offer a practical route to physically consistent, real-time temperature forecasting for battery safety systems. The multi-feature input set and explicit enforcement of thermal diffusion constraints address a recognized weakness of purely data-driven models in safety-critical applications.

major comments (3)

[Abstract] Abstract: the reported 81.9% RMSE and 81.3% MAE reductions are presented without any information on the value or selection procedure for the physics regularization weight λ, nor on whether a single fixed λ was used across all thirteen datasets or whether per-dataset tuning was performed. This directly affects the claim of generalization across diverse operating conditions.
[Abstract] Abstract and presumed experimental section: no ablation isolating the contribution of the physics term is described, nor are error bars, statistical significance tests, or variance across runs reported. Without these, it is impossible to determine whether the large error reductions are attributable to the heat-transfer constraint or to other modeling choices.
[Methodology] Methodology (loss-function description): the discretization of the governing heat-transfer equations into the regularization term and the precise manner in which thermal diffusion constraints are enforced on the LSTM predictions are not specified. This omission makes it difficult to assess whether the term introduces new inconsistencies or simply acts as an additional hyperparameter.

minor comments (1)

[Abstract] Abstract: the list of input features is helpful, but a short statement of the number of samples or operating-condition ranges covered by the thirteen datasets would strengthen the generalization claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of clarity and rigor in our presentation. We address each major comment below and will revise the manuscript accordingly to strengthen the work.

read point-by-point responses

Referee: [Abstract] Abstract: the reported 81.9% RMSE and 81.3% MAE reductions are presented without any information on the value or selection procedure for the physics regularization weight λ, nor on whether a single fixed λ was used across all thirteen datasets or whether per-dataset tuning was performed. This directly affects the claim of generalization across diverse operating conditions.

Authors: We agree that the abstract and main text currently lack explicit details on λ. In the revised manuscript we will state that a single fixed value of λ was used across all thirteen datasets, selected via preliminary validation experiments to balance predictive accuracy against physical consistency. This clarification will be added to the abstract and methodology to better support the generalization claims. revision: yes
Referee: [Abstract] Abstract and presumed experimental section: no ablation isolating the contribution of the physics term is described, nor are error bars, statistical significance tests, or variance across runs reported. Without these, it is impossible to determine whether the large error reductions are attributable to the heat-transfer constraint or to other modeling choices.

Authors: The current manuscript does not include an ablation isolating the physics term or report error bars and statistical tests. We will revise the experimental section to add an ablation study (PI-LSTM with and without the regularization term), report mean and standard deviation over five independent runs, and include paired statistical significance tests to confirm that the improvements stem from the physics constraint. revision: yes
Referee: [Methodology] Methodology (loss-function description): the discretization of the governing heat-transfer equations into the regularization term and the precise manner in which thermal diffusion constraints are enforced on the LSTM predictions are not specified. This omission makes it difficult to assess whether the term introduces new inconsistencies or simply acts as an additional hyperparameter.

Authors: We acknowledge that the exact discretization and enforcement details are insufficiently specified. In the revised methodology we will provide the finite-difference discretization of the heat equation used in the regularization term and describe how the constraint is applied directly to the LSTM temperature predictions at each time step, demonstrating that it enforces physical consistency without introducing new inconsistencies. revision: yes

Circularity Check

0 steps flagged

No circularity: physics term from external equations, performance from held-out experiments

full rationale

The PI-LSTM loss augments standard LSTM training with a regularization term taken directly from governing heat-transfer PDEs (external to the training data). Reported RMSE/MAE reductions are measured on thirteen separate battery datasets after training; no equation, prediction, or performance metric is shown to equal a fitted hyperparameter or self-citation by algebraic identity. The central empirical claim therefore remains independent of the paper's own fitted values.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that standard heat transfer equations can be turned into a differentiable loss term that improves rather than harms generalization; no new entities are introduced and the only potential free parameter is the physics regularization weight whose value is not reported.

axioms (1)

domain assumption Governing heat transfer equations can be discretized and added as a differentiable regularization term without introducing inconsistencies or requiring dataset-specific re-derivation
This is the core mechanism described for the PI-LSTM framework

pith-pipeline@v0.9.0 · 5577 in / 1422 out tokens · 60233 ms · 2026-05-12T03:42:17.531665+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Lphys = 1/N ∑ [ (T̂_{t+1}−T̂_t)/Δt − α (T̂_{t+1}−2T̂_t + T̂_{t−1}) ]² ; Ltotal = Ldata + λ Lphys
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

81.9% RMSE reduction on 13 datasets with physics regularization

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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