Dr. Mauro Maggioni: Geometric methods for learning global reaction coordinates and fast simulators of high-dimensional dynamical systems

Abstract

We discuss techniques for studying, in a quantitative fashion, certain properties of high-dimensional dynamical systems in view of performing model reduction, while preserving short and large time properties of the system. In particular, we will discuss techniques for estimating, in a robust fashion, an effective number of degrees of freedom of the system, which may vary in the state space of the system, and a local scale where the dynamics is well-approximated by a reduced dynamics with a small number of degrees of freedom. We use these ideas in two ways:

1. Given long trajectories of the system, to produce an approximation to the propagator of the system and obtain reaction coordinates for the system that capture the large time behavior of the dynamics, with applications to the automatic construction of reaction coordinates from molecular dynamics data. This is joint work with C. Clementi’s lab (Chemistry, Rice)
2. To learn, given local short parallel simulations, a family of local approximations to the system, that can be pieced together to form a fast global reduced model for the system, for which we can guarantee (under suitable assumptions) that large time accuracy is bounded by the small time accuracy of the local simulators. We discuss applications to homogenization of rough diffusions in low and high dimensions. This is joint work with M. Crosskey (Duke)

Biography

Dr. Mauro Maggioni works at the intersection between harmonic analysis, approximation theory, probability, machine learning, spectral graph theory, and statistical signal processing. He received his B.Sc. in Mathematics summa cum laude at the Universitá degli Studi in Milano in 1999, the Ph.D. in Mathematics from the Washington University, St. Louis, in 2002. He then was a Gibbs Assistant Professor in Mathematics at Yale University till 2006, when he moved to Duke University, where is now Professor in Mathematics, Electrical and Computer Engineering, and Computer Science. He received the Popov Prize in Approximation Theory in 2007, a N.S.F. CAREER award and Sloan Fellowship in 2008, and was nominated Fellow of the American Mathematical Society in 2013. He is a member of the A.M.S. and S.I.A.M.