Problem
Research questions and friction points this paper is trying to address.
Physics-Informed Neural Networks
Elastic Wave Equation
Seismology
Convergence
Accuracy
Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment
🤖 AI Summary
本文评估了物理信息神经网络（PINNs）在解决地震学中的弹性波方程问题上的表现，通过嵌入物理原理改进网络架构，提高了求解精度。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Physics-Informed Neural Networks
Elastic Wave Equation
Custom Wavelet Layer
Seismic Source Conditioning
Convergence and Accuracy
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