Geometry-Agnostic Data-Driven Discovery of Extreme Scenarios

Angeline Hu, Ava K. Tse, Kaitlyn S. Yasumura, Luciana Sarabia, Malcolm Yeung +6

We introduce a two-stage data-driven neural framework for discovering dynamically admissible extreme scenarios. Rather than assuming prior knowledge of the governing equations, the first stage infers the effective dynamical constraints directly from observational data. When the underlying physical system possesses suitable symmetries, the learned dynamics can be represented in a geometry-agnostic form, independent of any fixed grid, coordinate system, dimensionality, and intrinsic curvature. In the second stage, a physics-informed neural-search uses this learned dynamics to uncover rare, high-impact coherent structures that may not have appeared in the original observations. We demonstrate this framework through representative examples of increasing dimensionality and geometric complexity. Starting from a traditionally learned Duffing dynamics, we find a homoclinic pulse as a plausible localized extreme scenario. Next, since the same equation also appears in the stationary nonlinear Schrodinger system, with the coordinate interpreted as space instead of time, this pulse becomes a standing soliton. We then retrain the first stage using a geometry-agnostic neural representation,…