提出新型神经网络，精准模拟复杂电热系统中多场耦合行为。
Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems
- 采用残差注意力结构捕捉多物理场局部耦合与陡变梯度。
- 在四个典型场景中误差最低，尤其在温度变化和界面复杂时表现更优。
- 适合需要高精度建模的新能源系统设计与优化研究者使用。
高效热管理与精确场预测对先进能源系统（如电水动力传输、微流体能量采集器、电驱动热调节器）的设计至关重要。然而，由于强非线性场耦合、温度依赖系数变化及复杂界面动态，稳态电热耦合多物理场系统的仿真对物理信息神经网络仍具挑战。本文提出残差注意力物理信息神经网络（RA-PINN），统一求解速度、压力、电势与温度场。通过整合统一五场算子形式、残差连接特征传播与注意力引导通道调制，该架构有效捕捉局部耦合结构与陡峭梯度。在四个代表性能源相关基准测试中评估：常系数耦合、间接压力测压约束、温度依赖输运、斜界面一致性。相比Pure-MLP、LSTM-PINN与pLSTM-PINN，RA-PINN在所有场景中均实现最低均方误差（MSE）、均方根误差（RMSE）与相对 $L_2$ 误差。尤其在界面主导与变系数条件下保持高结构保真度，传统PINN主干常失效。结果表明，RA-PINN为可持续能源应用中复杂电热多物理场高保真建模与优化提供稳健准确的计算框架。
原文摘要 · Abstract (English)
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.
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