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

TL;DR

This paper introduces a parameter-embedded Fourier Neural Operator (PE-FNO) that significantly improves the speed and generalization of lithium-ion battery simulations, enabling real-time digital twins with high accuracy.

Contribution

The paper proposes a novel PE-FNO model that conditions spectral layers on physical parameters, enhancing generalization and speed over existing neural operators for battery simulation.

Findings

PE-FNO is approximately 200 times faster than traditional solvers.

PE-FNO maintains low concentration and voltage errors across various load types.

Parameter embedding enables generalization to different particle radii and diffusivities.

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.