2025/10/16 by Jimmie Adriazola, Adriazola, Jimmie, P. G. Kevrekidis +5
Computer Science · Materials Science · Physics and Astronomy · #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Machine Learning in Materials Science #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2510.15069
openalex publication_date 2025/10/16 · openalex created_date 2025/10/21 · openalex updated_date 2026/08/01
The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of the rapidly evolving landscape of scientific machine learning, including deep learning, data-driven equation discovery, \colorblue Koopman-based methods, and operator learning, among others. We then showcase these methods in applications ranging from learning lattice dynamical models and reduced order modeling of effective dynamics to discovery of conservation laws and potential identification of integrability of ODE and PDE models. Our intention is to make clear that these machine learning methods are complementary to the preexisting powerful tools of the nonlinear waves community, and should be integrated into this toolkit to augment and enable mathematical discoveries and computational capabilities in the age of data.