Physics‐Informed Deep Learning for Forward and Inverse Modeling of Inplane Crustal Deformation - Okazaki, Tomohisa; Hirahara, Kazuro; Ito, Takeo; Kano, Masayuki; Ueda, Naonori (Journal of geophysical research. Machine learning and computation, 2025)
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: (a) inplane deformation, which is typically used for modeling subduction zones, and (b) 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. Plain Language Summary Earthquakes and tectonic plate motions cause permanent deformation of the Earth's crust, which is called crustal deformation. Analysis of crustal deformation advances the understanding of earthquake preparation and rupture processes. In this study, we developed a method for analyzing crustal deformation using a deep learning method called physics‐informed neural networks (PINNs), which can solve both forward and inverse problems by designing optimization processes based on physical equations and observational data. Specifically, we focused on inplane crustal deformation, which is typically applied to plate subduction zones by assuming uniformity of crustal structures and deformation in the trench‐parallel direction. We verified that the PINNs demonstrated effective performance in both forward and inverse problems. Notably, in the inversion analysis of fault slips, PINNs yielded stable results without explicit mathematical regularization, which is required besides physical constraints for conventional inversion methods to suppress overfitting. This suggests an inherent regularization effect in PINNs, with potential implications for inversion analyses. Key Points Physics‐informed neural networks (PINNs) perform well in the forward and inverse modeling of inplane crustal deformation PINNs yield stable inversion results without explicit regularization, which may result from solving the governing equations PINNs may exhibit physics‐based regularization effects and hold potential for solving underdetermined nonlinear inverse problems