Physics-Informed Neural Networks with Hard Constraints for Axial Temperature Distribution Estimation of Lithium-Ion Batteries

Accurate estimation of the internal spatial-temporal temperature distribution is crucial for the safety and performance management of lithium-ion batteries. However, traditional lumped parameter models overlook spatial gradients, while numerical methods for partial differential equations (PDEs) incur high computational costs. This paper proposes a hard constraint physics-informed neural network (HCPINN) framework for the real-time reconstruction of the axial temperature field in 18,650 cylindrical batteries. By restructuring the neural network’s solution space through distance functions, the Robin boundary conditions are strictly embedded as hard constraints, ensuring exact satisfaction of the prescribed Robin boundary conditions within the mathematical model and eliminating boundary loss terms. An electro-thermal coupled model considering the Arrhenius effect and state-of-charge (SOC) dependent internal resistance is integrated into the loss function to capture the nonlinear heat generation dynamics. Experimental validation across discharge rates from 1C to 4C demonstrates that the HCPINN achieves high estimation accuracy with a mean absolute error (MAE) below 0.34 °C. Furthermore, by leveraging the continuous differentiability of the model, this study quantifies the evolution of spatial temperature gradients and reveals the ideal heat transfer coefficients required for thermal equilibrium are inverted, providing a quantitative basis for the design of advanced battery thermal management systems (BTMS).