Physics-informed optical convolution and mixture-of-experts learning for noninvasive lithium-ion battery state-of-health estimation

The accurate estimation of battery state of health (SOH) is essential for the reliable operation and management of battery energy storage systems. In practice, SOH estimation is challenging owing to heterogeneous battery populations, nonstationary degradation behavior, and the limited interpretability of many data-driven models. To address this issue, a physics-informed SOH estimation framework is proposed herein. This framework integrates frequency-modulated decomposition, multiscale optical convolution based on Fourier-optical principles, and a soft-gated mixture-of-experts (MoEs) architecture. Post-charge relaxation voltage signals are decomposed into intrinsic oscillatory components and enhanced in the frequency domain to extract degradation-sensitive features across multiple time scales. A dual-branch network jointly models temporal degradation dynamics and operating context information, whereas the soft-gated MoEs enables adaptive expert specialization across different aging stages and battery types. Experimental results demonstrate that the framework achieves robust, stable SOH prediction across the full SOH range, including advanced aging conditions. Interpretability is embedded directly into the model architecture via physically meaningful feature processing and expert-specific responses, providing insights consistent with underlying electrochemical degradation mechanisms. Thus, the proposed framework is well-suited for practical battery health monitoring and condition-aware energy management applications.