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arxiv: 2606.28220 · v1 · pith:W5WQ724Tnew · submitted 2026-06-26 · 💻 cs.LG

Physics-Informed Neural Network with Transfer Learning for State Estimation in Lithium-Ion Batteries using the Single Particle Model with Electrolyte

Gift Modekwe , Qiugang Lu This is my paper

Pith reviewed 2026-06-29 04:21 UTC · model grok-4.3

classification 💻 cs.LG
keywords physics-informed neural networkstransfer learningsingle particle model with electrolytelithium-ion batteriesstate estimationvoltage predictionelectrochemical consistency
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The pith

Transfer learning adapts pretrained SPMe-PINNs to new lithium-ion batteries by moving weights, freezing layers, and fine-tuning while preserving 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 that a physics-informed neural network based on the single particle model with electrolyte can be pretrained on general electrochemical dynamics and then transferred to a specific battery. This process involves transferring weights, freezing selected layers, and fine-tuning the rest to estimate key variables and predict voltage. The approach addresses slow convergence when training such networks from scratch for different chemistries or conditions. Validation with PyBaMM confirms accurate voltage predictions that maintain conservation laws inside the loss function.

Core claim

The central claim is that pretraining an SPMe-PINN on general electrochemical dynamics, followed by weight transfer, layer freezing, and targeted fine-tuning, produces accurate voltage predictions for target batteries while preserving electrochemical consistency, shortening training time, and supporting generalization across chemistries and operating conditions.

What carries the argument

The transfer learning framework for SPMe-PINNs that pretrains on general dynamics then transfers weights, freezes selected layers, and fine-tunes remaining parameters to adapt to a target battery.

If this is right

  • Accurate voltage prediction holds across different battery chemistries after adaptation.
  • Training time decreases compared with training an SPMe-PINN from scratch for each new battery.
  • Electrochemical consistency remains enforced through the PINN loss function during and after transfer.
  • Generalization to new operating conditions becomes feasible without full retraining.

Where Pith is reading between the lines

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

  • The same pretrain-and-transfer pattern could shorten setup time for other reduced-order electrochemical models beyond SPMe.
  • Faster adaptation might support online state estimation tasks where battery parameters drift over time.
  • Layer freezing choices could be studied to identify which parts of the network encode chemistry-independent physics.

Load-bearing premise

A model pretrained on general electrochemical dynamics can be adapted to a specific battery by transferring weights, freezing some layers, and fine-tuning the rest without losing physical consistency or accuracy for that chemistry or set of conditions.

What would settle it

Fine-tuning after transfer produces voltage predictions that violate the enforced conservation laws in the loss function or show larger errors than training an SPMe-PINN from scratch on the target battery data.

Figures

Figures reproduced from arXiv: 2606.28220 by Gift Modekwe, Qiugang Lu.

Figure 1
Figure 1. Figure 1: Schematics of the SPMe model. 2.1 Solid-Phase Diffusion In the SPMe, lithium-ion diffusion within the active material particles of positive (p) and negative (n) elec￾trodes is governed by Fick’s second law in spherical co￾ordinates: ∂cs,k ∂t = Ds,k r 2 k ∂ ∂rk  r 2 ∂cs,k ∂rk  , k ∈ {n, p}, (1) where cs,k(r,t) denotes the solid-phase lithium concen￾tration, Ds,k is the solid diffusivity, and r is the radi… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the proposed transfer learning [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between the PyBaMM SPMe model and the transfer learning in the SPMe-PINN framework for B2 showing (a) terminal voltage predic￾tion at a 1C discharge rate, (b) negative electrode solid￾phase lithium concentration, (c) positive electrode solid￾phase lithium concentration, and (d) terminal voltage prediction at a 0.5C discharge rate. To further assess the robustness, we evaluate the model under a d… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of terminal voltage predictions [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the PyBaMM SPMe model and the proposed transfer learning SPMe-PINN framework for the B3 showing (a) terminal voltage pre￾diction at 1C discharge rate and (b) terminal voltage prediction at 1.2C discharge rate. 4.4 Parameter Estimation To evaluate the parameter identification capability of the proposed framework, the solid-phase diffusivities are modeled as learnable parameters during tra… view at source ↗
read the original abstract

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving nonlinear partial differential equations (PDEs), including battery electrochemical models. They typically en-force conservation laws within the loss function to ensure physically consistent solutions. Tradi-tional numerical methods such as finite difference, finite volume, and finite element techniques, re-ly on discretization and can be computationally expensive for nonlinear systems. To address this challenge, PINNs offer improved scalability, particularly for reduced-order models like the single particle model with electrolyte (SPMe). The SPMe describes lithium-ion battery dynamics through coupled diffusion, transport, reaction kinetics, and voltage equations. Despite these advantages, training SPMe-based PINNs from scratch for different battery chemistries or operating conditions is demanding and often leads to slow convergence. To overcome this limitation, this work introduces a transfer learning framework for SPMe-PINNs. The model is first pretrained to learn general elec-trochemical dynamics and then adapted to a target battery by transferring weights, freezing se-lected layers, and fine tuning the remaining parameters, including estimating key electrochemical variables. Validation using PyBaMM demonstrates accurate voltage prediction, indicating that the proposed approach preserves electrochemical consistency while reducing training time and ena-bling efficient generalization across batteries.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a transfer-learning framework for SPMe-based physics-informed neural networks (PINNs). A model is pretrained on general electrochemical dynamics, after which weights are transferred to a target battery, selected layers are frozen, and the remainder are fine-tuned (including estimation of key electrochemical variables). Validation against PyBaMM is reported to yield accurate voltage predictions, from which the authors conclude that electrochemical consistency is preserved, training time is reduced, and generalization across batteries is enabled.

Significance. If the central claim holds, the work would address a practical bottleneck in applying PINNs to battery models by avoiding full retraining for each chemistry or operating condition. The approach could improve scalability for reduced-order electrochemical models, provided the physics-informed constraints survive the transfer step.

major comments (2)
  1. [Abstract] Abstract: the claim that 'accurate voltage prediction' indicates preservation of electrochemical consistency is unsupported. Voltage is a single derived output; the SPMe comprises multiple coupled PDEs (solid diffusion, electrolyte transport, Butler-Volmer kinetics). No evidence is presented that the physics-informed loss terms or residuals on these governing equations remain small after weight transfer, layer freezing, and fine-tuning. This verification is load-bearing for the central claim.
  2. [Abstract] Abstract / Validation section: the manuscript states that PyBaMM validation 'demonstrates accurate voltage prediction' but supplies no quantitative metrics (RMSE, MAE, error bars), no baseline comparisons (e.g., full retraining, other transfer strategies), and no details on how physical consistency was checked beyond the terminal voltage. Without these, the empirical support for the transfer-learning benefit cannot be assessed.
minor comments (1)
  1. [Abstract] Abstract: the phrasing 'including estimating key electrochemical variables' is ambiguous; clarify whether these variables are outputs of the fine-tuned network or additional supervised targets.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights opportunities to strengthen the empirical support for our transfer-learning claims. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'accurate voltage prediction' indicates preservation of electrochemical consistency is unsupported. Voltage is a single derived output; the SPMe comprises multiple coupled PDEs (solid diffusion, electrolyte transport, Butler-Volmer kinetics). No evidence is presented that the physics-informed loss terms or residuals on these governing equations remain small after weight transfer, layer freezing, and fine-tuning. This verification is load-bearing for the central claim.

    Authors: We agree that the abstract's phrasing over-relies on terminal voltage as a proxy. Although the PINN loss includes the full set of SPMe residuals during both pretraining and fine-tuning, the manuscript does not report post-transfer residual norms for the individual PDEs. In revision we will add a dedicated subsection (or appendix) showing the evolution of the physics residuals for solid-phase diffusion, electrolyte concentration, and Butler-Volmer kinetics before and after transfer, thereby directly substantiating that electrochemical consistency is retained. revision: yes

  2. Referee: [Abstract] Abstract / Validation section: the manuscript states that PyBaMM validation 'demonstrates accurate voltage prediction' but supplies no quantitative metrics (RMSE, MAE, error bars), no baseline comparisons (e.g., full retraining, other transfer strategies), and no details on how physical consistency was checked beyond the terminal voltage. Without these, the empirical support for the transfer-learning benefit cannot be assessed.

    Authors: We concur that the current validation description is insufficient for readers to evaluate the claimed benefits. The revised manuscript will include: (i) explicit RMSE/MAE values with error bars for voltage predictions on the target battery, (ii) direct comparisons against a from-scratch SPMe-PINN baseline and at least one alternative transfer strategy, and (iii) a concise description of the additional consistency checks (residual norms and selected internal electrochemical variables) that will be reported. These additions will be placed in both the abstract and the validation section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical workflow validated externally

full rationale

The paper describes a transfer-learning workflow for SPMe-PINNs without presenting any derivation chain, equations, or fitted parameters that reduce claimed outputs to inputs by construction. The assertion that voltage accuracy 'indicates' preserved consistency is an empirical inference drawn from PyBaMM simulations, not a self-referential tautology. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps. The result therefore stands as an independent empirical claim against an external benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The approach implicitly assumes that electrochemical dynamics are sufficiently general to transfer and that PyBaMM provides an independent ground-truth benchmark.

pith-pipeline@v0.9.1-grok · 5760 in / 1032 out tokens · 37435 ms · 2026-06-29T04:21:02.778485+00:00 · methodology

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Reference graph

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