Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML) excels in the presence of large data and is an actively growing field in seismology. However, not all ML methods incorporate rigorous physics, and purely data-driven models can predict physically unrealistic outcomes due to observational bias or extrapolation. Our work focuses on the recently emergent Physics-Informed Neural Network (PINN), which seamlessly integrates data while ensuring that model outcomes satisfy rigorous physical constraints. In this work we develop a multi-network PINN for both the forward problem as well as for direct inversion of nonlinear fault friction parameters, constrained by the physics of motion in the solid Earth, which have direct implications for assessing seismic hazard. We present the computational PINN framework for strike–slip faults in 1D and 2D subject to rate-and-state friction. Initial and boundary conditions define the data on which the PINN is trained. While the PINN is capable of approximating the solution to the governing equations to low-errors, our primary interest lies in the network’s capacity to infer friction parameters during the training loop. We find that the network for the parameter inversion at the fault performs much better than the network for material displacements to which it is coupled. Additional training iterations and model tuning resolves this discrepancy, enabling a robust surrogate model for solving both forward and inverse problems relevant to seismic faulting.

中文翻译：

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基于物理的速率和状态断层摩擦深度学习


对地震成核和传播的直接观测很少，但未来十年可能会看到必须纳入建模工作的间接地面观测前所未有的增加。机器学习 (ML) 在大数据方面表现出色，是地震学中一个积极发展的领域。然而，并非所有机器学习方法都包含严格的物理学，并且纯粹的数据驱动模型可以预测由于观察偏差或外推而导致的物理上不切实际的结果。我们的工作重点是最近出现的物理信息神经网络（PINN），它无缝集成数据，同时确保模型结果满足严格的物理约束。在这项工作中，我们开发了一个多网络 PINN，用于正演问题以及非线性断层摩擦参数的直接反演，受固体地球运动物理的约束，这对评估地震危险性具有直接影响。我们提出了受速率和状态摩擦影响的一维和二维走滑断层的计算 PINN 框架。初始条件和边界条件定义了 PINN 训练所依据的数据。虽然 PINN 能够以低误差逼近控制方程的解，但我们的主要兴趣在于网络在训练循环期间推断摩擦参数的能力。我们发现断层参数反演网络的性能比与其耦合的材料位移网络要好得多。额外的训练迭代和模型调整解决了这种差异，从而实现了强大的替代模型来解决与地震断层相关的正向和逆向问题。