Fast and Generalizable parameter-embedded Neural Operators for Lithium-Ion Battery Simulation

2025/08/11 by Daniel Luder, Panahi, Amir Ali, Billy Wu +8
Engineering · #Advanced Battery Technologies Research #Advancements in Battery Materials #Chemical Physics (physics.chem-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Low-power high-performance VLSI design #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2508.08087

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Reliable digital twins of lithium-ion batteries must achieve high physical fidelity with sub-millisecond speed. In this work, we benchmark three operator-learning surrogates for the Single Particle Model (SPM): Deep Operator Networks (DeepONets), Fourier Neural Operators (FNOs) and a newly proposed parameter-embedded Fourier Neural Operator (PE-FNO), which conditions each spectral layer on particle radius and solid-phase diffusivity. Models are trained on simulated trajectories spanning four current families (constant, triangular, pulse-train, and Gaussian-random-field) and a full range of State-of-Charge (SOC) (0 % to 100 %). DeepONet accurately replicates constant-current behaviour but struggles with more dynamic loads. The basic FNO maintains mesh invariance and keeps concentration errors below 1 %, with voltage mean-absolute errors under 1.7 mV across all load types. Introducing parameter embedding marginally increases error, but enables generalisation to varying radii and diffusivities. PE-FNO executes approximately 200 times faster than a 16-thread SPM solver. Consequently, PE-FNO's capabilities in inverse tasks are explored in a parameter estimation task with Bayesian optimisation, recovering anode and cathode diffusivities with 1.14 % and 8.4 % mean absolute percentage error, respectively, and 0.5918 percentage points higher error in comparison with classical methods. These results pave the way for neural operators to meet the accuracy, speed and parametric flexibility demands of real-time battery management, design-of-experiments and large-scale inference. PE-FNO outperforms conventional neural surrogates, offering a practical path towards high-speed and high-fidelity electrochemical digital twins.

Citations

• Learning Neural PDE Solvers with Parameter-Guided Channel Attention
• Machine learning pipeline for battery state of health estimation
• Fourier Neural Operator for Parametric Partial Differential Equations
• Universal Differential Equations for Scientific Machine Learning
• Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
• An asymptotic derivation of a single particle model with electrolyte
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• SGDR: Stochastic Gradient Descent with Warm Restarts
• Deep Residual Learning for Image Recognition
• Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
• Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell

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