arXiv:2609.07983cs.LG2026-09

用物理先验神经网络求解地震波方程,显著提升精度与稳定性。

Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment

论文配图:Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment
图 1 · 摘自论文原文
  • 将波动物理知识融入网络结构,设计专用波形层提升性能。
  • 相对L2误差降低约一半,优于标准PINN在复杂地质中的表现。
  • 可快速定位震源,适用于地震灾害快速评估场景。

物理信息神经网络(PINNs)作为求解偏微分方程的新兴方法,提供了一种无需网格的替代方案,将物理规律嵌入学习过程。尽管前景广阔,但其仍面临谱偏差和收敛不稳定等挑战,尤其在地震学中的应用尚未深入探索。本文对PINNs求解地震弹性波方程进行了系统且严格的评估,涵盖从均匀到高度非均质介质的多种震源与参数模型。研究重点在于:将物理知识直接嵌入网络架构是否能改善收敛性与精度。通过测试从通用到高度定制化的多种网络设计,发现引入自定义小波或平面波层,并结合编码器-解码器结构,可使相对L2误差稳定降至标准PINN的一半。该架构在声波方程上也表现出色,验证了其普适性。此外,成功实现对震源位置的精准条件化,为地震快速危害探测与分析提供了重要进展。

原文摘要 · Abstract (English)

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for solving Partial Differential Equations (PDEs), offering a meshfree alternative that integrates physical principles into the learning process. This presents a new paradigm compared to traditional discretization methods and purely data-driven machine learning techniques. While promising, PINNs are not a panacea; they inherit challenges such as spectral bias and unstable convergence. Moreover, their potential in seismology remains largely unexplored. In this work, we provide a robust and critical assessment of PINNs for solving the elastic wave equation in seismology. We investigate the performance of PINNs on problems with varying degrees of complexity across various seismic sources and parameter models, from constant to highly heterogeneous settings. A pivotal aspect of our work involves investigating whether embedding physical principles directly into the network architecture enhances convergence and accuracy. We test an extensive range of neural architecture designs, from unrestricted, uninformed PINNs to highly specialized ones. We find that integrating an understanding of wave physics into the network design significantly improves accuracy. For instance, introducing a custom wavelet or plane wave layer, coupled with encoder and decoder layers, consistently yields a relative $L_2$ error approximately half that of the standard PINN, as evidenced across numerous experiments. We further demonstrate that this novel architecture enhances accuracy when applied to the acoustic wave equation, underlying the versatility of our network. Another key contribution of our research is the successful conditioning of PINNs on seismic source locations. This signifies a considerable advancement towards rapid seismic hazard detection and seismic analysis.

物理信息网络地震波模拟神经网络架构波场建模

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