标题： 机器学习非线性波：用于计算机辅助发现方程、对称性、守恒定律和可积性的数据驱动方法 显示英文标题

标题： Machine Learning of Nonlinear Waves: Data-Driven Methods for Computer-Assisted Discovery of Equations, Symmetries, Conservation Laws, and Integrability

摘要： 本文的目的是提供一个视角——尽管这无疑是一个相当主观的视角——关于机器学习/数据驱动方法与非线性波研究交叉领域的最新发展。 我们回顾了科学机器学习快速发展的领域中的一些近期支柱，包括深度学习、数据驱动方程发现和算子学习等。 然后，我们将这些方法应用于从学习格子动力学模型和有效动力学的降阶建模到发现守恒定律以及识别常微分方程和偏微分方程模型的可积性的各种应用。 我们的意图是明确这些机器学习方法是对非线性波领域现有强大工具的补充，并应整合到该工具箱中，以增强和推动数据时代数学发现和计算能力。 显示英文摘要

摘要： 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, 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.