将物理规律嵌入网络结构,加速大尺度波场重建。
Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction
- 在神经网络架构中直接融入波场物理特性,超越传统损失函数约束。
- 收敛速度提升10倍以上,内存消耗比FEM降低数个数量级。
- 适合无线通信、声学传感等需大域波场建模的工程场景。
大尺度波场重建需要高精度解法,但面临计算效率与准确性的双重挑战。基于物理的数值方法如有限元法(FEM)虽精度高,却因计算成本过高难以应对大规模或高频问题;纯数据驱动方法虽快速,但在复杂场景下常缺乏足够标注数据。物理信息神经网络(PINNs)通过将物理规律引入机器学习模型,有望弥合此差距。然而标准PINNs仅在损失函数中嵌入物理约束,导致收敛慢、优化不稳定及频谱偏差,限制其在大尺度波场重建中的应用。本文提出架构式物理嵌入(PE)-PINN,不仅在损失函数中包含亥姆霍兹方程与边界条件,更将源特性、介质界面和波物理参数以可学习核形式直接嵌入网络架构。设计了一种新的包络变换层,有效缓解频谱偏差。实验表明,相较于标准PINNs,PE-PINN收敛速度提升超10倍,内存占用较FEM降低数个数量级。该方法实现了室级2D/3D电磁波场的高保真重建,涵盖反射、折射与衍射,适用于无线通信、传感、室内声学等需要大尺度波场分析的领域。
原文摘要 · Abstract (English)
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.
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