C–PINN: A Coupled Physics‐Informed Neural Network for Solving Parabolic Two‐Step Models in Electron–Lattice Thermal Conduction

This paper introduces a coupled physics‐informed neural network (C–PINN) framework for simulating electron–lattice thermal conduction. The framework uses an additive Δ‐decomposition to couple the electron temperature T e and lattice temperature T l , with a learnable correction term Δ( t , x ) capturing spatial–temporal deviations from thermal equilibrium. Additionally, a residual‐balanced and localized adaptive refinement (RLAR) strategy is employed to enhance model accuracy and training efficiency, especially in high‐error regions. Numerical experiments demonstrate the model’s robustness across different Knudsen numbers ( K n ) and boundary conditions, showing its ability to capture fine‐grained temperature deviations and optimize high‐error regions through dynamic adaptive sampling.