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

2025-08-11

AI Summary

To address the stringent requirements of real-time lithium-ion battery simulation—namely, high computational speed, prediction accuracy, and parameter generalizability—this work proposes a Parameter-Embedded Fourier Neural Operator (PE-FNO). PE-FNO explicitly incorporates particle radius and solid-phase diffusion coefficient into its spectral layers, enabling strong generalization across physical parameters. Trained against the Single-Particle Model (SPM) ground truth, it learns concentration and voltage dynamics across the full state-of-charge range under diverse operating conditions (constant-current, triangular-wave, pulsed, and stochastic current profiles). Compared to a 16-thread SPM solver, PE-FNO achieves ~200× acceleration while maintaining <1% concentration prediction error and <1.7 mV voltage MAE. It further enables Bayesian diffusion coefficient inversion with anode/cathode errors of 1.14% and 8.4%, matching conventional methods’ accuracy. This is the first application of parameter embedding in neural operators for electrochemical modeling, enabling high-fidelity, sub-millisecond digital twins and robust inverse parameter estimation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Mixture of Experts (MoE)

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Developing fast neural operators for lithium-ion battery simulation
• Achieving high accuracy and speed in battery digital twins
• Enabling parameter generalization for real-time battery management

Innovation

• Parameter-embedded Fourier Neural Operator (PE-FNO)
• Generalizes to varying radii and diffusivities
• Executes 200 times faster than SPM solver