Ming Zhong
Texas A&M University
Thursday, October 28, 2021
3:30 pm - 4:30 pm
Join Zoom Meeting
https://notredame.zoom.us/j/99326826419?pwd=c0Y2NEJmaFAydnZBUnFnQ1hDMmhyQT09
Meeting ID: 993 2682 6419
Passcode: 551832
This talk will be presented via Zoom. The talk will also be projected on the monitors in 101A Crowley Hall and refreshments will be provided.
Title: Machine Learning of Collective Behaviors from Observation
Abstract:
Collective behaviors (or self-organization) can be found in crystal formation, aggregation of cells/animals, social behaviors of insects and humans, etc. It is a challenging task to understand such behaviors from the mathematical point of view. We offer a statistical/machine learning approach to understand these behaviors quantitatively from observation data; moreover, our learning approach can aid in validating and improving the modeling of collective behaviors.
We develop a learning framework to derive physically meaningful models to explain the observations data using dynamical systems. We provide a convergence theory in terms of the number of different initial conditions for first-order systems of homogeneous agents, and investigate its performance for various first- and second-order systems of heterogeneous agents. We also study the stead state properties of our learned models, and extend the learning framework to include more complicated structures. We extend the approach to learn dynamical models for agents constrained on Riemannian manifolds.
Having successfully applied our learning method to various set of simulated data, we study the effectiveness of our learning method on the National Aeronautics and Space Administration Jet Propulsion Laboratory’s modern Ephemerides. We discover that our learned model outperforms the Newton’s model (based on Newton’s universal law of gravitation) in terms of reproducing the position/velocity of major celestial bodies, as well as preserving geometric properties (period/aphelion/perihelion) of the trajectory and highly- localized perihelion precession rates of Mars, Mercury, and the Moon. Upon careful inspection of our model, we discover that it even captures potion of the general relativity effects.