Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems

Abstract

Efficient thermal management and precise field prediction are critical for the design of advanced energy systems, including electrohydrodynamic transport, microfluidic energy harvesters, and electrically driven thermal regulators. However, the steady-state simulation of these electrothermal coupled multiphysics systems remains challenging for physics-informed neural computation due to strong nonlinear field coupling, temperature-dependent coefficient variability, and complex interface dynamics. This study proposes a Residual Attention Physics-Informed Neural Network (RA-PINN) framework for the unified solution of coupled velocity, pressure, electric-potential, and temperature fields. By integrating a unified five-field operator formulation with residual-connected feature propagation and attention-guided channel modulation, the proposed architecture effectively captures localized coupling structures and steep gradients. We evaluate RA-PINN across four representative energy-relevant benchmarks: constant-coefficient coupling, indirect pressure-gauge constraints, temperature-dependent transport, and oblique-interface consistency. Comparative analysis against Pure-MLP, LSTM-PINN, and pLSTM-PINN demonstrates that RA-PINN achieves superior accuracy, yielding the lowest MSE, RMSE, and relative $L_2$ errors across all scenarios. Notably, RA-PINN maintains high structural fidelity in interface-dominated and variable-coefficient settings where conventional PINN backbones often fail. These results establish RA-PINN as a robust and accurate computational framework for the high-fidelity modeling and optimization of complex electrothermal multiphysics in sustainable energy applications.

Figures (5)

• Figure 1: Workflow of the RA-PINN solver used in this study. The schematic organizes the method into six coupled parts: governing equations and computational domain, adaptive residual sampling, residual-attention PINN mapping, residual adaptation, gradient-based optimization, and prediction/validation. The uploaded schematic uses generic space-time notation; in the present steady-state problem the network input reduces to the spatial coordinate $(x,y)$ and the outputs reduce to the five coupled fields $\hat{u}$, $\hat{v}$, $\hat{p}$, $\hat{\phi}$, and $\hat{T}$.
• Figure 2: Uploaded benchmark comparison for Case 1. The top strip reports the loss-history comparison, the five rows correspond to $p$, $u$, $v$, $\phi$, and $T$, the left block reports the benchmark and predicted fields, and the right block reports the absolute-error maps of the four learned solvers.
• Figure 3: Uploaded benchmark comparison for Case 2. This benchmark replaces direct pressure anchoring with a zero-mean gauge constraint, so the figure tests how each network reconstructs the five coupled fields under indirect pressure identifiability.
• Figure 4: Uploaded benchmark comparison for Case 3. This benchmark activates temperature-dependent transport coefficients, so the figure directly tests how well each network resolves variable-coefficient coupling across the five physical fields.
• Figure 5: Uploaded benchmark comparison for Case 4. The benchmark contains an oblique material interface, so the figure highlights interface-sensitive reconstruction quality by placing the learned absolute-error maps next to the predicted multiphysics fields.