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Molei Tao


Speaker: Molei Tao
Title: Towards the Control of Multiscale Stochastic Systems
Affiliation: Courant Institute, New York University
Date: Monday, Febuary 3, 2014
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract Motivated by rich applications in science and engineering, I am interested in controlling systems that are characterized by multiple scales, geometric structures, and randomness. This talk will focus on my first two steps towards this goal. The first step is to be able to simulate these systems. We developed integrators that do not resolve fast scales in these systems but still capture their effective contributions. These integrators require no identification of underlying slow variables or processes, and therefore work for a broad spectrum of systems (including stiff ODEs, SDEs and PDEs). They also numerically preserve intrinsic geometric structures (e.g., symplecticity, invariant distribution, and other conservation laws), and this leads to improved long time accuracy. The second step is to understand what noises can do and utilize them. We quantify noise-induced transitions by optimizing probabilities given by Freidlin-Wentzell large deviation theory. In gradient systems, transitions between metastable states were known to cross saddle points. We investigate nongradient systems, and show transitions may instead cross unstable periodic orbits. Numerical tools for identifying periodic orbits and for computing transition paths are proposed. I will also describe how these results help design control strategies.