PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model

TL;DR

A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals, and explore the Bayesian calibration capabilities of both surrogates.

Abstract

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

Figures (11)

• Figure 1: Illustrative PINN architecture used to enforce spatiotemporal dependencies of the state variables for the single-particle model. PINN inputs are in black rectangles, while outputs are in blue rectangles. White rectangles denote blocks of hidden layers that could be of any type (see Sec. \ref{['sec:arch']}).
• Figure 1: Average PINN relative error $\varepsilon$ (darker bar) and terminal voltage error $\varepsilon_{\rm TV}$ computed with Eq. \ref{['eq:errtv']} (lighter bar) for different current conditions. The error bar denotes the 95% percentile variability observed for all the realizations.
• Figure 2: Training loss history for 23 realizations of an SPM PINN surrogate using only the physics loss.
• Figure 2: Hybrid electric vehicle drive cycle considered.
• Figure 3: Conditional average of the PINN error conditioned on the weight $w_{c_{\rm s,int}}$ for the collocation points located in the interior of the SPM spatial domain (a, d), the collocation points located at the $r=0$ boundary (b, e) and the collocation points located at the $r=R_{{\rm max},j}$ boundary (c, f). Weight initialization is Glorot normal (a, b, c) and He normal (d, e, f).