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

arXiv:2603.02231v1 Announce Type: new 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 beyon

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Huiwen Zhang, Feng Ye, Chu Ma · · 1 min read · 9 views
#cs.LG #cs.AI

arXiv:2603.02231v1 Announce Type: new 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.

Executive Summary

This article presents a novel approach to large-scale wave field reconstruction by integrating physical principles into the neural network architecture. The proposed Physics Embedded (PE)-PINN achieves significant speedup in convergence and memory usage reduction compared to standard Physics-Informed Neural Networks (PINNs) and Finite Element Method (FEM). The envelope transformation layer mitigates spectral bias, enabling high-fidelity modeling for complex scenarios. This breakthrough has wide-ranging implications for wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.

Key Points

  • ▸ The authors propose a new architecture, Physics Embedded (PE)-PINN, which integrates physical principles directly into the neural network architecture.
  • ▸ The 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.
  • ▸ The envelope transformation layer mitigates spectral bias and enables high-fidelity modeling for complex scenarios.

Merits

Strength

The PE-PINN architecture provides a promising solution for large-scale wave field reconstruction by bridging the gaps between computational efficiency and accuracy.

Strength

The envelope transformation layer effectively mitigates spectral bias and enables high-fidelity modeling for complex scenarios.

Demerits

Limitation

The proposed method relies on the accuracy of physical parameters and material interfaces, which may introduce errors or uncertainties in modeling real-world scenarios.

Limitation

The method may require significant computational resources for training and deployment, particularly for large-scale wave field reconstruction.

Expert Commentary

The article presents a significant breakthrough in large-scale wave field reconstruction, leveraging the power of physics-informed neural networks. The proposed PE-PINN architecture effectively integrates physical principles into the neural network architecture, mitigating spectral bias and enabling high-fidelity modeling for complex scenarios. While there are potential limitations, including reliance on accurate physical parameters and material interfaces, the PE-PINN has the potential to revolutionize various fields requiring large-scale wave field analysis. The implications are far-reaching, with potential applications in wireless communications, sensing, and room acoustics.

Recommendations

  • ✓ Further research is needed to investigate the scalability and robustness of the PE-PINN architecture for large-scale wave field reconstruction.
  • ✓ The authors should explore the application of the PE-PINN in other fields, such as medical imaging and geophysics, where large-scale wave field analysis is critical.

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