The episodic transient fault slips called slow slip events (SSEs) have been observed in many subduction zones. These slips often occur in regions adjacent to the seismogenic zone during the interseismic period, making monitoring SSEs significant for understanding large earthquakes. Various fault slip behaviors, including SSEs and earthquakes, can be explained by the spatial heterogeneity of frictional properties on the fault. Therefore, estimating frictional properties from geodetic observations and physics-based models is crucial for fault slip monitoring. In this study, we propose a Physics-Informed Neural Network (PINN)-based new approach to simulate fault slip evolutions, estimate frictional parameters from observation data, and predict subsequent fault slips. PINNs, which integrate physical laws and observation data, represent the solution of physics-based differential equations. As a first step, we validate the effectiveness of the PINN-based approach using a simple single-degree-of-freedom spring-slider system to model SSEs. As a forward problem, we successfully reproduced the temporal evolution of SSEs using PINNs and obtained implications on how to choose the appropriate collocation points by analyzing the residuals of physics-based differential equations. As an inverse problem, we estimated the frictional parameters from synthetic observation data and demonstrated the ability to obtain accurate values regardless of the choice of first-guess values. Furthermore, we discussed the potential of the predictability of the subsequent fault slips using limited observation data, taking into account uncertainties. Our results indicate the significant potential of PINNs for fault slip monitoring.

Methods for modeling crustal deformation related to earthquakes and plate motions have been developed to incorporate complex crustal structures and multi-fidelity observations. A machine learning approach called physics-informed neural networks (PINNs), which can solve both forward and inverse problems of physical systems, was proposed and applied to the forward simulations of antiplane deformation. Here, we aimed to extend the PINN approach to crustal deformation in two directions: (1) inplane deformation, which is typically used for modeling subduction zones, and (2) inversion analysis of fault slips from geodetic observations. We verified the performance of PINNs on these problems and suggested that formulations in Cartesian and polar coordinates are suitable for forward and inverse modeling, respectively. Furthermore, PINNs yielded stable inversion results without explicit regularization terms, implying that solving the governing equations with PINNs implicitly imposes regularization based on the physical requirements. This may elucidate the distinctive properties of PINNs and provide insights into inversion analyses in geophysics and other fields.

Slow slip events (SSEs) have been observed in many subduction zones and are understood to result from frictional unstable slip on the plate interface. The diversity of their characteristics and the fact that interplate slip can also be seismic suggest that frictional properties are heterogeneous. We are however lacking methods to constrain spatial distribution of frictional properties. In this paper, we employ Physics-Informed Neural Networks (PINNs) to achieve this goal using a synthetic model inspired by the long-term SSEs observed in the Bungo channel. PINN is a deep learning technique which can be used to solve the physics-based differential equations and determine the model parameters from observations. To examine the potential of our proposed method, we execute a series of numerical experiments. We start with an idealized case where it is assumed that fault slip is directly observed. We next move to a more realistic case where the synthetic surface displacement velocity data are observed by virtual GNSS stations. The geometry and friction properties of the velocity weakening region, where the slip instability develops, are well estimated, especially if surface displacement velocities above the velocity weakening region are observed. Our PINN-based method can be seen as an inversion technique with the regularization constraint that fault slip obeys a particular friction law. This approach remediates the issue that standard regularization techniques are based on non-physical constraints. These results of numerical experiments reveal that the PINN-based method is a promising approach for estimating the spatial distribution of friction parameters from GNSS observation.