PINEAPPLE: Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter Inference in Lithium-Ion Battery Electrodes

TL;DR

PINEAPPLE (Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter inference in Lithium-ion battery Electrodes) is introduced, a novel framework that integrates physics-informed neural networks (PINNs) with an evolutionary search algorithm to enable rapid, scalable, and interpretable parameter inference with potential for application to next-generation batteries.

Abstract

Accurate, real-time, yet non-destructive estimation of internal states in lithium-ion batteries is critical for predicting degradation, optimizing usage strategies, and extending operational lifespan. Here, we introduce PINEAPPLE (Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter inference in Lithium-ion battery Electrodes), a novel framework that integrates physics-informed neural networks (PINNs) with an evolutionary search algorithm to enable rapid, scalable, and interpretable parameter inference with potential for application to next-generation batteries. The meta-learned PINN utilizes fundamental physics principles to achieve accurate zero-shot prediction of electrode behavior with test errors below 0.1$\%$ while maintaining an order-of-magnitude speed-up over conventional solvers. PINEAPPLE demonstrates robust parameter inference solely from voltage-time discharge curves across multiple batteries from the open-source CALCE repository, recovering the evolution of key internal state parameters such as Li-ion diffusion coefficients across usage cycles. Notably, the inferred cycle-dependent evolution of these parameters exhibit consistent trends across different batteries without any customized degradation physics-embedded heuristic, highlighting the effective regularizing effect and robustness that can be conferred through incorporation of fundamental physics in PINEAPPLE. By enabling computationally efficient, real-time parameter estimation, PINEAPPLE offers a promising route towards the non-destructive, physics-based characterization of inter-cell and intra-cell variability of battery modules and battery packs, thereby unlocking new opportunities for downstream on-the-fly needs in next-generation battery management systems such as individual cell-scale state-of-health diagnostics.

Figures (9)

• Figure 1: Discharge voltage-time (V-t) curves for the four selected CX2 batteries. A red-to-blue gradient color scheme is used to distinguish V-t curves across different cycles (CALCE CX2-34: 50--1726 cycles, CX2-36: 53--1958 cycles, CX2-37: 53--1274 cycles, CX2-38: 53--1949 cycles) during the battery's degradation process, with the progression in cycles indicated by a change in color from blue to green to orange and finally red.
• Figure 2: PINEAPPLE schematic. The nonlinear hidden layers of LE-PINN are meta-learned (pre-trained) through Baldwinian neuroevolution, which takes less than 600 seconds on a sparse simulation dataset with diffusion coefficients ($D_k$) spanning 3 orders of magnitude. The fine-tuning (forward solve) of the final layer for positive and negative electrodes together costs less than 20 milliseconds for specific SPM parameters. The evolutionary search for best fit cycle-dependent parameters to match the observed V-t curve, $V^{obs}$, can be completed in a few seconds. Representative examples for early-, mid-, and late-cycle experimentally observed V-t curves (obtained from CALCE CX2-37 Cycle 53, Cycle 638, and Cycle 1181 respectively) and the corresponding prediction from the PINEAPPLE framework are illustrated in the top portion of the Figure.
• Figure 3: Predictive performance of LE-PINN model: examples of the solution vs. ground truth for unseen (top: out-of-sample, bottom: out-of-distribution) SPM parameters for positive and negative electrodes. The concentrations $C_p$ and $C_n$ are normalized by their respective initial values.
• Figure 4: Comparison of relative error and computational time between LE-PINN (obtained via fine-tuning of the final layer) and numerical solver from PyBaMM at different mesh resolutions, using an out-of-sample SPM parameter for the positive electrode as a representative example. LE-PINN achieves comparable accuracy to that of the numerical solution with a mesh size of 32, while requiring significantly less (10$\times$) computational time. For all cases, errors are computed with respect to the reference numerical solution generated by PyBaMM using a mesh size of 1024.
• Figure 5: Simulated discharge V-t curves (dashed) using different SPM and terminal voltage calculation parameters. These curves are used for a preliminary evaluation before conducting inverse inference on the real-world dataset. The simulated curves correspond well qualitatively to the early (blue), middle (green), and late (red) cycles of the battery degradation process. The range of measured V-t curves, from the real dataset as described in Section \ref{['sec:dataset']}, is shown in the background as semi-transparent solid lines.