Prof. Naonori Ueda

“Physics-Informed Deep Learning Approach for Modeling Crustal Deformation”

 Thursday March 9, 2023 | Time 9:30am CET

The movement and deformation of the Earth’s crust and upper mantle provide critical insights into the evolution of earthquake processes and future earthquake potentials. Crustal deformation can be modeled by dislocation models that represent earthquake faults in the crust as defects in a continuum medium. In this talk, let me introduce a novel physics-informed deep learning approach to model crustal deformation due to earthquakes. Neural networks can represent continuous displacement fields in arbitrary geometrical structures and mechanical properties of rocks by incorporating governing equations and boundary conditions into a loss function. The polar coordinate system is introduced to accurately model the displacement discontinuity on a fault as a boundary condition. I will show the validity and usefulness of this approach through example problems with strike-slip faults. This approach has a potential advantage over conventional approaches in that it could be straightforwardly extended to high dimensional, anelastic, nonlinear, and inverse problems.

In this talk, we describe our recent research that has demonstrated that the non-convex optimization dogma is false by showing that scalable stochastic optimization algorithms can avoid traps and rapidly obtain locally optimal solutions. Coupled with the progress in representation learning, such as over-parameterized neural networks, such local solutions can be globally optimal.

Unfortunately, this talk will also demonstrate that the central min-max optimization problems in ML, such as generative adversarial networks (GANs), robust reinforcement learning (RL), and distributionally robust ML, contain spurious attractors that do not include any stationary points of the original learning formulation. Indeed, we will describe how algorithms are subject to a grander challenge, including unavoidable convergence failures, which could explain the stagnation in their progress despite the impressive earlier demonstrations. We will conclude with promising new preliminary results from our recent progress on some of these difficult challenges.