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Direct observations of earthquake nucleation and propagation are few and yetthe next decade will likely see an unprecedented increase in indirect, surfaceobservations that must be integrated into modeling efforts. Machine learning(ML) excels in the presence of large data and is an actively growing field inseismology. However, not all ML methods incorporate rigorous physics, andpurely data-driven models can predict physically unrealistic outcomes due toobservational bias or extrapolation. Our work focuses on the recently emergentPhysics-Informed Neural Network (PINN), which seamlessly integrates data whileensuring that model outcomes satisfy rigorous physical constraints. In thiswork we develop a multi-network PINN for both the forward problem as well asfor direct inversion of nonlinear fault friction parameters, constrained by thephysics of motion in the solid Earth, which have direct implications forassessing seismic hazard. We present the computational PINN framework forstrike-slip faults in 1D and 2D subject to rate-and-state friction. Initial andboundary conditions define the data on which the PINN is trained. While thePINN is capable of approximating the solution to the governing equations tolow-errors, our primary interest lies in the network's capacity to inferfriction parameters during the training loop. We find that the network for theparameter inversion at the fault performs much better than the network formaterial displacements to which it is coupled. Additional training iterationsand model tuning resolves this discrepancy, enabling a robust surrogate modelfor solving both forward and inverse problems relevant to seismic faulting.

Physics-Informed Deep Learning of Rate-and-State Fault Friction