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

arXiv: https://arxiv.org/abs/2603.23578 · HTML: https://mlsanity.com/paper/2603.23578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2501.16371/) (2025)
- [Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?](https://mlsanity.com/paper/2405.04230/) (2024)
- [One-shot learning for solution operators of partial differential equations](https://mlsanity.com/paper/2104.05512/) (2021)
- [Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks](https://mlsanity.com/paper/2407.01613/) (2024)
- [Diffeomorphism Neural Operator for various domains and parameters of partial differential equations](https://mlsanity.com/paper/2402.12475/) (2024)
- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [Exact Enforcement of Temporal Continuity in Sequential Physics-Informed Neural Networks](https://mlsanity.com/paper/2403.03223/) (2024)
- [Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2411.15111/) (2024)
- [A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning](https://mlsanity.com/paper/2509.14198/) (2025)
- [LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks](https://mlsanity.com/paper/2508.08935/) (2025)

## Abstract (arXiv)

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 L2 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.