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

TL;DR

This paper introduces PE-PINN, an architecture-embedded physics-informed neural network that significantly improves large-scale wave field reconstruction by enhancing convergence speed and reducing memory usage, surpassing traditional PINNs and FEM.

Contribution

The work presents a novel PE-PINN architecture with an envelope transformation layer that embeds physical guidance directly into the neural network, addressing spectral bias and convergence issues.

Findings

PE-PINN achieves over 10x faster convergence than standard PINNs.

PE-PINN reduces memory usage by several orders of magnitude compared to FEM.

Enables high-fidelity large-scale electromagnetic wave modeling in complex environments.

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.