Application of Physics-Informed Neural Networks to spring-slider model with rate and state friction

Abstract

In the Physics-Informed Neural Networks (PINNs) approach, we construct neural networks that can solve the physics-based equations by minimizing the loss function which involves the differential equations of the physics law and initial / boundary conditions [Raissi et al., 2019]. This approach has been recently adopted to many research fields because it can solve not only forward problems but also inverse problems easily. In seismology, a spring-slider model is often used to simulate the fault slip evolution [Yoshida and Kato, 2003]. In this study, we adopted PINNs to the spring-slider model that combines quasi-dynamic equations of motion and rate and state friction law [Ruina, 1983], and attempted to reproduce slow slip events (SSEs). Unlike the time adaptive Runge-Kutta approach that is usually adopted in solving these equations, PINNs can solve the equation with the equidistant collocation points. To incorporate the temporal causal structure, we also applied the Causal-PINNs [Wang et al., 2022] to the same problem. In addition, we estimated the frictional parameters by adding the misfit term between the observed and calculated slip velocity data to the loss function. These results imply that PINNs approach is effective to earthquake cycle simulation and frictional parameter estimation.