Probabilistic Modeling of Dynamical Systems

Abstract

Complex dynamical systems are ubiquitous in the physical world. Mathematically, they are described with ordinary or partial differential equations, derived from physical laws. In most cases, analytic solutions to those differential equations are not attainable. As such, numerical computing techniques are often used to solve them. For systems that are complex and large-scale, however, classical methods are computationally expensive, especially when high accuracy is desired.

In this talk, I will give 3 vignettes of our recent research efforts in using machine learning technology to overcome the challenge, by complementing the strengths of the traditional scientific computing methods. In particular, I will show how probabilistic modeling techniques such as neural parameterized stochastic differential equations, probabilistic diffusion models, and optimal transport can be utilized to reduce the computational costs yet provide statistically reliable forecast and prediction of such systems' future behavior.

This talk is based on several joint works with my colleagues at Google Research.

Bio:

Dr. Sha is a Research Scientist at Google Research. He leads a team of scientists and engineers, focusing on research in foundational AI and machine learning, scientific machine learning, and AI for Weather and Climate. Prior to joining Google Research, Dr. Sha was a professor at University of Southern California. Dr. Sha obtained his Ph.D in Computer and Information Science from University of Pennsylvania. More information about Dr. Sha's scholastic activities can be found at his microsite at http://feisha.org.