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A Residual-Attention Physics-Informed Neural Network for Irregular Interfaces and Multi-Peak Transport Fields

Baitong Zhou, Ze Tao, Fujun Liu, Xuan Fang

Abstract

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical methods often suffer from high computational latency, whereas standard Physics-Informed Neural Networks (PINNs) frequently fail to capture critical local features, such as irregular interfaces, localized high-gradient regions, and multi-peak transport structures. To address these limitations and provide high-fidelity intelligent predictions for engineering decision-making, this paper proposes a Residual-Attention Physics-Informed Neural Network (RA-PINN) as a powerful surrogate modeling engine. The proposed method incorporates residual learning and attention enhancement into the network backbone to improve the representation of oblique transition structures, narrow charge layers, and distributed hotspots while strictly preserving global field consistency. To evaluate its effectiveness as an intelligent prediction framework, three representative benchmark cases are constructed, including an oblique asymmetric interface, a bipolar high-gradient charge layer, and a multi-peak Gaussian charge migration field. Under unified training settings, the proposed RA-PINN is systematically compared with a standard pure PINN and an LSTM-PINN in terms of average error, local maximum error, structural similarity, and convergence behavior. The results show that RA-PINN consistently achieves the best overall performance across all benchmark cases, demonstrating its tremendous potential as a highly reliable core inference engine for the condition monitoring and digital twin modeling of complex multi-physics engineering systems.

A Residual-Attention Physics-Informed Neural Network for Irregular Interfaces and Multi-Peak Transport Fields

Abstract

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical methods often suffer from high computational latency, whereas standard Physics-Informed Neural Networks (PINNs) frequently fail to capture critical local features, such as irregular interfaces, localized high-gradient regions, and multi-peak transport structures. To address these limitations and provide high-fidelity intelligent predictions for engineering decision-making, this paper proposes a Residual-Attention Physics-Informed Neural Network (RA-PINN) as a powerful surrogate modeling engine. The proposed method incorporates residual learning and attention enhancement into the network backbone to improve the representation of oblique transition structures, narrow charge layers, and distributed hotspots while strictly preserving global field consistency. To evaluate its effectiveness as an intelligent prediction framework, three representative benchmark cases are constructed, including an oblique asymmetric interface, a bipolar high-gradient charge layer, and a multi-peak Gaussian charge migration field. Under unified training settings, the proposed RA-PINN is systematically compared with a standard pure PINN and an LSTM-PINN in terms of average error, local maximum error, structural similarity, and convergence behavior. The results show that RA-PINN consistently achieves the best overall performance across all benchmark cases, demonstrating its tremendous potential as a highly reliable core inference engine for the condition monitoring and digital twin modeling of complex multi-physics engineering systems.
Paper Structure (23 sections, 25 equations, 4 figures, 7 tables)

This paper contains 23 sections, 25 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Governing Equations and Problem Description
  3. Governing equations
  4. Benchmark formulation with known reference solutions
  5. Boundary conditions, supervised data, and learning objective
  6. Residual-Attention PINN Method
  7. PINN formulation and compared models
  8. Residual-attention network architecture
  9. Training strategy
  10. Benchmark Cases and Experimental Settings
  11. Benchmark design
  12. Case 1: Oblique asymmetric interface
  13. Case 2: Bipolar high-gradient charge layer
  14. Case 3: Multi-peak Gaussian charge migration field
  15. Experimental settings and evaluation metrics
  16. ...and 8 more sections

Figures (4)

  • Figure 1: Schematic architecture of the proposed residual-attention physics-informed neural network (RA-PINN). The network takes the spatial coordinates $(x,y)$ as input and predicts five coupled physical fields $(u,v,p,T,\phi)$. Automatic differentiation is used to compute the required spatial derivatives and construct the PDE residuals for physics-informed training. As shown in the residual-attention module, the hidden feature is processed through a residual-feature branch and an attention-gate branch, where the gate is generated from the block input and adaptively modulates the feature branch before residual addition, followed by layer normalization. This design improves the representation of irregular interfaces, localized high-gradient regions, and multi-peak field structures while preserving global feature propagation.
  • Figure 2: Visual comparison for Case 1, including field prediction, absolute error, and log-scale loss evolution.
  • Figure 3: Visual comparison for Case 2, including field prediction, absolute error, and log-scale loss evolution.
  • Figure 4: Visual comparison for Case 3, including field prediction, absolute error, and log-scale loss evolution.