用物理信息神经网络求解弹性波方程：一项稳健而严格的评估
Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment
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中文总结 AI 辅助
本文对物理信息神经网络（PINNs）求解弹性波方程进行了稳健严格的评估，发现将波动物理融入网络设计（如自定义小波层）可将相对L2误差减半，并成功将震源位置条件化，推动快速地震检测。
中文摘要 AI 辅助
物理信息神经网络（PINNs）近年来作为一种求解偏微分方程（PDEs）的有前景的方法出现，提供了一种将物理原理融入学习过程的无网格替代方案。与传统离散化方法和纯数据驱动的机器学习技术相比，这提出了一种新的范式。尽管前景广阔，但PINNs并非万能；它们继承了谱偏差和收敛不稳定等挑战。此外，它们在地震学中的潜力在很大程度上尚未被探索。在这项工作中，我们对PINNs用于求解地震学中的弹性波方程进行了稳健而严格的评估。我们研究了PINNs在具有不同复杂程度的问题上的性能，这些问题的震源和参数模型各不相同，从恒定到高度非均匀的设置。我们工作的一个关键方面是研究将物理原理直接嵌入网络架构是否能增强收敛性和准确性。我们测试了广泛的神经架构设计，从无约束、无信息的PINNs到高度专门化的PINNs。我们发现，将波动物理的理解融入网络设计显著提高了准确性。例如，引入自定义小波或平面波层，并结合编码器和解码器层，始终产生相对$L_2$误差约为标准PINN的一半，这在众多实验中得到了证实。我们进一步证明，这种新颖的架构在应用于声波方程时也能提高准确性，凸显了我们网络的通用性。我们研究的另一个关键贡献是成功地将PINNs条件化于地震源位置。这标志着向快速地震危险检测和地震分析迈出了重要一步。
英文摘要
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.
发表机构
- ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
