Improving physics-informed training for forward and inverse problems in earthquake dynamics

Cody Rucker

Submitted September 7, 2025, SCEC Contribution #14850, 2025 SCEC Annual Meeting Poster #TBD

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML) excels in the presence of large data and is an actively growing field in seismology. However, not all ML methods incorporate rigorous physics, and purely data-driven models can predict physically unrealistic outcomes due to observational bias or extrapolation. Our work focuses on the recently emergent Physics-Informed Neural Network (PINN), which seamlessly integrates data while ensuring that model outcomes satisfy rigorous physical constraints. However, the prescribed boundary conditions in a well-posed initial boundary value problem give rise to multi-objective loss functions that complicate network training. Here we implement a generalized transfinite interpolation for exact enforcement of space-time boundary conditions in a 2D vector wave problem. This approach uses an implicit representation of the domain boundaries which allows for exact enforcement over complex geometries but alters the solution behavior in important ways: solution derivatives are not defined along the hard-enforced boundary, and the solution is singular at points where distinct boundaries overlap. This first issue is resolved by considering the one-sided limit approaching the boundary from the domain interior but the second issue leads us to consider key alterations to the problem’s formulation. The size of the Laplacian of the interpolating bases in a neighborhood of the singularity makes training difficult near boundary corners. This suggests that any reformulation of the problem into a lower-order PDE may find greater success. In particular, we believe a formulation that avoids hard enforcement on solution derivatives to be ideal as it avoids recursive derivatives in the general solution form.

Key Words
deep learning, physics-informed neural network, numerical pde, analytic geometry

Citation
Rucker, C. (2025, 09). Improving physics-informed training for forward and inverse problems in earthquake dynamics. Poster Presentation at 2025 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)