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

AI summary

Overview

Research area: computational engineering, lithium-ion battery modeling, physics-informed machine learning, and evolutionary optimization. Technical level: Advanced. Scope: The paper introduces PINEAPPLE, a physics-informed neuro-evolution framework that infers cycle-dependent internal electrochemical parameters in lithium-ion battery electrodes from voltage-time measurements alone. It is published as arXiv:2602.18042v1 [cs.CE] 20 Feb 2026 and associated with the Journal of Energy Storage.

What This Paper Is About

Accurate, real-time, and non-destructive estimation of internal lithium-ion battery states is important for predicting degradation, optimizing usage, and extending operational lifespan. Physics-based models such as the single-particle model (SPM) link measurable voltage response to internal electrochemical dynamics, but they are computationally costly and require parameters that are difficult to measure or infer during operation. The paper’s goal is to enable rapid, robust, and interpretable inverse inference of key internal parameters, such as lithium-ion diffusion coefficients, directly from real-world voltage-time discharge curves.

Key Contributions

1. The authors introduce PINEAPPLE, a physics-informed neuro-evolution framework that combines meta-learned physics-informed neural networks with evolutionary search for rapid, non-destructive inference of internal electrochemical state parameters in lithium-ion batteries from voltage-time measurements alone.
2. They employ a Baldwinian meta-learning strategy to train a highly generalizable PINN model for the SPM that achieves zero-shot, physics-consistent prediction of electrode lithium-ion concentration dynamics with 10× speed-up over PyBAMM at similar accuracies.
3. They formulate non-destructive inverse inference of internal state parameters from V-t data across cycles as an evolutionary search over physically meaningful scaling factors, enabling fast and robust parameter inference without battery-specific calibration.
4. They demonstrate recovery of consistent and physically interpretable degradation trends in key internal parameters such as effective anode and cathode diffusion coefficients using real-world data from the open-source CALCE dataset.

Main Findings

• Zero-shot prediction accuracy: The meta-learned PINN uses 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.
• Speed-up over PyBAMM: The LE-PINN can achieve 10× speed-up over PyBAMM at similar accuracies.
• Fast meta-learning and inference: Meta-learning takes less than 600 seconds on a sparse simulation dataset with diffusion coefficients spanning 3 orders of magnitude. Fine-tuning 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 can be completed in a few seconds.
• Real-world parameter recovery: 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.
• Consistent degradation trends: The inferred cycle-dependent evolution of these parameters exhibits consistent trends across different batteries without any customized degradation physics-embedded heuristic, highlighting the effective regularizing effect and robustness conferred by incorporating fundamental physics in PINEAPPLE.
• Inferred parameters: Four cycle-dependent scaling factors are inferred: η_Dp, η_Dn, η_Gp, and η_cmax,p, corresponding to the positive electrode diffusion coefficient, negative electrode diffusion coefficient, positive electrode geometrical composite coefficient, and positive electrode maximum lithium-ion concentration.
• Dataset and cycling details: The study uses four CX2 battery cells from CALCE: CX2-34, CX2-36, CX2-37, and CX2-38. The V-t curves span cycles 50–1726, 53–1958, 53–1274, and 53–1949 respectively. Cells were cycled with a constant current rate of 0.5C until voltage reached 4.2V, held at 4.2V until charging current decreased below 0.05A, then discharged at 1.35A until a discharge cut-off voltage of 2.7V.
• Voltage-time behavior: Initial V-t curves exhibit a well-defined, long-lasting voltage plateau. As the battery ages, the voltage plateau shifts leftward, indicating capacity fade. Near end of life, voltage drops much more rapidly and the curve becomes irregular or highly sloped.
• Representative cycles: The paper illustrates early-, mid-, and late-cycle experimentally observed V-t curves from CALCE CX2-37 Cycle 53, Cycle 638, and Cycle 1181, with corresponding PINEAPPLE predictions.

Methodology in Plain English

The authors start from the SPM, which treats lithium-ion diffusion in each electrode as diffusion inside a representative spherical particle, governed by Fick’s Law of Diffusion. Solving the SPM gives surface lithium-ion concentrations, which are then used in a terminal voltage equation that includes equilibrium potentials, over-potentials, and lumped internal resistance. Because publicly available data such as CALCE lack precise electrode properties, the method introduces scaling factors for parameters including diffusion coefficient, geometrical composite coefficient, maximum lithium-ion concentration, initial lithium-ion concentration, particle radius, and exchange current density. The inference problem is reduced to finding four cycle-dependent scaling factors for Dp, Dn, Gp, and cmax,p.

PINEAPPLE has two stages. In the offline meta-learning stage, a Lithium-ion battery Electrochemical Physics-Informed Neural Network (LE-PINN) is meta-learned using Baldwinian neuroevolution. The LE-PINN is a shallow network with a single hidden layer using sin, silu, and tanh activations. The hidden-layer weights are drawn from a probability distribution controlled by a reduced set of hyperparameters. An outer evolutionary optimization loop searches for hidden-layer weights and learning hyperparameters that generalize across sampled SPM conditions, while an inner physics-informed fine-tuning step solves only the final linear layer. Because the SPM equations are linear with respect to concentration, this final-layer solve uses a Tikhonov-regularized pseudo-inverse least-squares formulation, giving a closed-form update with no ground-truth labels needed. The outer-loop loss weights are fixed at τ_LSE = 0.1 and τ_MSE = 1.0. The meta-learning process runs on a workstation with 4× NVIDIA L40 GPUs, and the CR-FM-NES optimizer with a JAX backend is used.

In the online inference stage, PINEAPPLE searches for the four scaling factors that minimize the squared distance between the measured V-t curve and the LE-PINN-predicted V-t curve. This is solved with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a gradient-free, population-based method that helps address the ill-posed inverse problem. The LE-PINN can be evaluated at irregularly sampled locations to align with measurement points, avoiding interpolation or subsampling.

Why This Matters

Impact on research: The work shifts the use of PINNs for batteries from model acceleration toward real-time parameter inference.

Authors’ 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.