11:15 AM - 11:30 AM
[SCG51-08] Solving Dislocation Models Using Physics-Informed Neural Networks
Recently, Raissi et al. (2019) introduced a physics-informed neural network (PINN) to solve partial differential equations (PDEs). By incorporating a target PDE and its boundary and initial conditions into a loss function using automatic differentiation, PINNs search for a latent solution without training data. Moreover, PINNs can be applied to both forward and inverse problems with almost identical network architectures, which is appealing to geophysical applications.
This study applies PINNs to dislocation models to obtain static crustal deformation caused by fault ruptures. A characteristic of dislocation models is that a displacement field is discontinuous across a dislocation surface and cannot be directly modeled by neural networks. We therefore set an appropriate coordinate system to separate coordinate values of the two sides of a displacement discontinuity.
In experiments, PINNs are applied to anti-plane problems (i.e. infinitely long strike-slip faults). We first compare PINN's solutions with analytical solutions (Segall, 2010) for simple problems on a vertical fault in the uniform half-space. We then solve complex problems such as curved faults, topography, and heterogeneous media for which analytical approaches are difficult. PINNs have an advantage that continuous shapes and variations can be modeled without discretization, in contrast to traditional methods such as the finite difference method and the finite element method. PINNs have a potential to solve a wide variety of modeling applications in crustal deformation.
This study applies PINNs to dislocation models to obtain static crustal deformation caused by fault ruptures. A characteristic of dislocation models is that a displacement field is discontinuous across a dislocation surface and cannot be directly modeled by neural networks. We therefore set an appropriate coordinate system to separate coordinate values of the two sides of a displacement discontinuity.
In experiments, PINNs are applied to anti-plane problems (i.e. infinitely long strike-slip faults). We first compare PINN's solutions with analytical solutions (Segall, 2010) for simple problems on a vertical fault in the uniform half-space. We then solve complex problems such as curved faults, topography, and heterogeneous media for which analytical approaches are difficult. PINNs have an advantage that continuous shapes and variations can be modeled without discretization, in contrast to traditional methods such as the finite difference method and the finite element method. PINNs have a potential to solve a wide variety of modeling applications in crustal deformation.