Lévy Jump Nonlocal SPDE and BA-PINN Modeling for Battery Fracture and Thermal-Runaway Warning

Electrode-particle fracture and thermal runaway remain major safety and durability challenges for lithium-ion batteries. Deterministic degradation models are limited in representing random crack nucleation, long-range crack interactions, and critical transitions from stable operation to failure. A computational framework is proposed that combines a Lévy-jump-driven nonlocal stochastic partial differential equation (SPDE) model with a Bifurcation-Aware Physics-Informed Neural Network (BA-PINN). The framework couples fractional diffusion, peridynamic damage evolution, thermal feedback, state-space eigenvalue tracking, and damage-variance monitoring. Evaluation is conducted on controlled synthetic fracture simulations, Oxford battery cycling records, and open-access abuse-test records from the Battery Failure Databank. The damage-field results are interpreted as numerical consistency and surrogate-learning evidence, with direct experimental crack-map validation remaining outside the present dataset scope. On the simulated fracture dataset, the proposed method obtains a damage-field mean squared error of 0.023 ± 0.002 and a structural similarity index of 0.962 ± 0.006. For the evaluated thermal-runaway warning task, it achieves an AUC-ROC of 0.987 ± 0.004 and an average model-inferred warning lead time of 5.2 ± 0.2 h. These results demonstrate the methodological feasibility of combining stochastic nonlocal fracture modeling with bifurcation-aware learning. However, broader validation remains necessary, particularly using particle-resolved experiments and larger event-level thermal-runaway datasets.