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Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction

Huiwen Zhang, Feng Ye, Chu Ma

TL;DR

High-fidelity modeling for large-scale 2D/3D electromagnetic wave reconstruction involving reflections, refractions, and diffractions in room-scale domains, readily applicable to wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.

Abstract

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with large-scale or high-frequency problems due to prohibitive computational costs. Pure data-driven approaches excel in speed but often lack sufficient labeled data for complex scenarios. Physics-informed neural networks (PINNs) integrate physical principles into machine learning models, offering a promising solution by bridging these gaps. However, standard PINNs embed physical principles only in loss functions, leading to slow convergence, optimization instability, and spectral bias, limiting their ability for large-scale wave field reconstruction. This work introduces architecture physics embedded (PE)-PINN, which integrates additional physical guidance directly into the neural network architecture beyond Helmholtz equations and boundary conditions in loss functions. Specifically, a new envelope transformation layer is designed to mitigate spectral bias with kernels parameterized by source properties, material interfaces, and wave physics. Experiments demonstrate that PE-PINN achieves more than 10 times speedup in convergence compared to standard PINNs and several orders of magnitude reduction in memory usage compared to FEM. This breakthrough enables high-fidelity modeling for large-scale 2D/3D electromagnetic wave reconstruction involving reflections, refractions, and diffractions in room-scale domains, readily applicable to wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.

Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction

TL;DR

High-fidelity modeling for large-scale 2D/3D electromagnetic wave reconstruction involving reflections, refractions, and diffractions in room-scale domains, readily applicable to wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.

Abstract

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with large-scale or high-frequency problems due to prohibitive computational costs. Pure data-driven approaches excel in speed but often lack sufficient labeled data for complex scenarios. Physics-informed neural networks (PINNs) integrate physical principles into machine learning models, offering a promising solution by bridging these gaps. However, standard PINNs embed physical principles only in loss functions, leading to slow convergence, optimization instability, and spectral bias, limiting their ability for large-scale wave field reconstruction. This work introduces architecture physics embedded (PE)-PINN, which integrates additional physical guidance directly into the neural network architecture beyond Helmholtz equations and boundary conditions in loss functions. Specifically, a new envelope transformation layer is designed to mitigate spectral bias with kernels parameterized by source properties, material interfaces, and wave physics. Experiments demonstrate that PE-PINN achieves more than 10 times speedup in convergence compared to standard PINNs and several orders of magnitude reduction in memory usage compared to FEM. This breakthrough enables high-fidelity modeling for large-scale 2D/3D electromagnetic wave reconstruction involving reflections, refractions, and diffractions in room-scale domains, readily applicable to wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.
Paper Structure (29 sections, 21 equations, 17 figures, 6 tables)

This paper contains 29 sections, 21 equations, 17 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Wave Physics in PE-PINN
  3. Wave Physics in PE-PINN Loss Function
  4. Helmholtz equation
  5. Boundary conditions
  6. Wave Physics in PE-PINN Architecture
  7. Envelop Transformation based on Wave Behavior
  8. Separation of Incident Field and Scattered Field
  9. Material-aware domain decomposition
  10. Methodology
  11. Overview of PE-PINN
  12. Envelop Transformation Layers
  13. Loss Function
  14. Sub-nets for Separating the Incident and Scattered Fields
  15. Sub-nets for Spatial Domains with Different Material Properties
  16. ...and 14 more sections

Figures (17)

  • Figure 1: Overview of the proposed PE-PINN.
  • Figure 2: Wave field reconstruction results for 2D free space with plane wave source (Scenario 1).
  • Figure 3: Wave field reconstruction results for 2D and 3D spherical wave diffraction (Scenario 7, 8).
  • Figure 4: Wave field reconstruction results for 2D and 3D spherical wave half space refraction (Scenario 9, 10).
  • Figure 5: Wave field reconstruction results for 2D plane wave source (Scenario 1).
  • ...and 12 more figures