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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 and initial / boundary conditions [Raissi et al., 2019]. This approach has been recently adopted in many research fields because it not only provides the mesh-free framework for forward problems but also easily obtains solutions for inverse problems. In seismology, a spring-slider model is often used to simulate fault slip evolution [Yoshida and Kato, 2003]. In this study, we applied PINNs to this simulation in the spring-slider model that combines quasi-dynamic equations of motion [Rice, 1993] and rate and state friction law [Ruina, 1983]. By assigning appropriate frictional parameters, we successfully reproduced slow slip events (SSEs). Unlike the time-adaptive Runge-Kutta approach that is usually used in solving these equations, PINNs can solve the equation with equidistant collocation points. This indicates the high interpolation ability of PINNs. To incorporate the temporal causal structure, we also applied the Causal-PINNs [Wang et al., 2022] to the same problem. We found that the Causal-PINNs obtained a similar simulation result with faster calculation speed and higher accuracy compared to original PINNs. In addition, we estimated the frictional parameters by adding the misfit term between the observed and calculated slip velocity data to the loss function. As a result, all frictional parameters are optimized from the synthetic data with added noises. These results imply that the PINNs approach is effective in earthquake cycle simulation and frictional parameter estimation.
