Physics-Informed Deep Learning of Rate-and-State Fault Friction
Cody Rucker Brittany A. Erickson
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.