A physics-informed neural network enhanced by fuzzy inference for remaining useful life prediction of lithium-ion batteries

Accurate prediction of the remaining useful life (RUL) of lithium-ion batteries (LIBs) is essential for ensuring the safety and reliability of energy storage systems. However, this task remains highly challenging due to measurement noise and the difficulty of maintaining physical consistency in purely data-driven models. To reconcile electrochemical physical fidelity with data adaptability, a physics-informed neural network (PINN) incorporating fuzzy inference system (FIS) enhancement is proposed, where a Takagi-Sugeno-Kang neuro-fuzzy (TSK-FIS) inference system is employed as a surrogate network to improve feature representation of nonlinear battery degradation. The resulting features are then fed into a Deep Hidden Physics Model (DeepHPM), the core physics-constrained component of the framework, within which an adaptive gated residual connection (AGRC) is embedded to tightly couple latent degradation dynamics with the network architecture. This structure effectively alleviates the error accumulation issue commonly encountered in long-horizon RUL prediction. Furthermore, to improve robustness against noise and outliers in battery data, a SoftAdapt-driven Cauchy–HawkEye loss function is designed. By introducing a small insensitive zone around the zero-residual region and adaptively balancing multiple loss components, the training stability and optimization robustness are significantly improved. Experimental results across multiple datasets indicate that the proposed method achieves superior overall predictive performance compared with baseline models, yielding a substantial reduction in RMSE while maintaining strong robustness and generalization capability.