Probabilistic Physics-Informed Battery Modeling Using Bayesian Neural Networks

Sammanfattning

A probabilistic physics-informed battery modelling framework based on Bayesian neural networks is presented to predict battery degradation and electrothermal behaviour under uncertainty. The framework combines simplified physical battery models with probabilistic residual learning to estimate internal resistance, capacity fade, temperature, state of charge (SOC), and terminal voltage. The modelling framework is formulated as a recursive state-space system in which physics-based equations describe the dynamics and Bayesian neural networks capture residual errors. Internal resistance and capacity are first estimated using fleet-level degradation models trained on cycle-level features, then propagated into recursive electrothermal models for temperature, SOC, and voltage prediction. Bayesian inference is performed using stochastic variational inference, enabling uncertainty propagation with computationally feasible recursive training. The results demonstrate that the proposed framework successfully combines physics-based modeling with probabilistic residual learning to predict battery degradation and electrothermal states under uncertainty. The thermal and voltage models achieved improved predictive accuracy compared with their corresponding physics-only models while providing uncertainty estimates throughout the prediction horizon. In contrast, the SOC model primarily benefited from uncertainty quantification rather than improved predictive accuracy, since the underlying Coulomb-counting formulation already captured most of the SOC dynamics. The thermal and SOC models benefited from the underlyingphysics-based state dynamics that stabilised recursive predictions and limited long-termuncertainty growth, whereas the voltage model showed greater uncertainty accumulation during extended rollouts. Prediction interval coverage was also influenced by initialisation bias and upstream degradation-model errors, with temperature affected by fixedambient-temperature initialisation and SOC at end of life impacted by propagated capacity overestimation. Overall, the framework demonstrates the value of combining physical structure with probabilistic learning for uncertainty-aware battery-state prediction, while highlighting the importance of stabilising constraints and careful uncertainty calibration in long-horizonrecursive modelling