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Geometry-Agnostic Data-Driven Discovery of Extreme Scenarios

Angeline Hu, Ava K. Tse, Kaitlyn S. Yasumura, Luciana Sarabia, Malcolm Yeung, Kavin K. Prasanna, Kai Wong, William Hammond, Ioannis G. Keverkidis, Shengkai Li, Trung V. Phan · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28487 · cited by 0 works (OpenAlex) · open-access PDF

Korean

우리는 심지어 두 단계의 균형 데이터를 통한 신경 구조를 도입하여 동적으로 허용되는 극단적 시나리오를 발견합니다. 위험 방정식에 대한 사전 지식을 가정하는 대신, 첫 번째 단계는 관측 데이터에서 직접 효과적인 동적 제약을 추출합니다. 기본적인 물리적 시스템이 적절한 동적을 보유할 때, 학습 된 동적 구조는 원래 관측에서 나타나지 않았을 수있는 기하학적 동적 형태로 표현될 수 있습니다. 우리는 어떤 고정된 그리드, 조정 체계, 차원성 및 내재적 복잡성을 나타내는 대표적인 예를 통해이 작업을 보여줍니다. 두 번째 단계에서, 물리학적으로 알려진 펄스 신경 검색은이 학습 된 동적 역학을 사용하여 희귀

Machine translation (Meta M2M100); the English original follows.

Abstract

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, enabling the learned dynamics to be lifted to higher-dimensional space to obtain higher-dimensional solitary profile, known as Townes soliton. Finally, with a Liouville system, we demonstrate that dynamics learned from data on a (1+1)-dimensional Lorentzian quasi-manifold can be transferred to a (2+0)-dimensional Euclidean manifold to identify an instanton. Our approach can be applied to other coherent spatiotemporal structures, including kinks, rogue waves, compactons, peakons, and potentially even singularities, with applications in risk analysis, nonlinear forecasting, and anomaly detection.

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Topics: Curse of dimensionality, Nonlinear system, Rogue wave, Euclidean space, Homoclinic orbit, Dynamical systems theory

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