Physics-informed Machine Learning of Collective Behaviors
报告题目(Title)：Physics-informed Machine Learning of Collective Behaviors
报告人(Speaker)：Ming ZHONG（Johns Hopkins University）
地点(Place)：ZOOM会议:ID:62574318088, Password: 497513
时间(Time)：5月24日（星期一），1:30pm-2:30pm
邀请人(Inviter)：蔡勇勇
报告摘要
Collective behaviors (clustering, flocking, milling, etc.) are among the most interesting and challenging phenomena to understanding from the mathematical point of view. We offer a non-parametric and physics-based learning approach to discover the governing structure, i.e. the interaction functions between agents, of collective dynamics from observation of the trajectory data. Our learning approach can aid in validating and improving the modeling of collective dynamics. We establish a learning framework which exploits the physical structure of the collective dynamical systems; hence the method demonstrates an optimal learning rate which is independent of the dimension of the observation data. We then investigate the steady state properties of the estimated dynamics for various first- and second-order models, and complete the second-order learning theory for extended models. Moreover, we extend our learning method to dynamics constrained on Riemannian manifolds. In order to further assess the capabilities of our learning method, we apply it to study celestial mechanics from NASA JPL’s development ephemerides. We are able to reproduce highly accurate trajectories, which preserve not long the geometric properties(period/aphelion/perihelion) of the orbits, but also the perihelion precession rate of three prototypical celestial bodies (Mars, Mercury and Moon).
