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Mathematics Colloquium by Molei Tao
Thursday, Jan 16
2 p.m. - 3 p.m. Location: GR 4.204

Molei Tao

Courant Institute

New York University

 Towards the control of multiscale stochastic systems

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 insteadcross 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.

Sponsored by the Department of Mathematical Sciences

Host: Sue Minkoff

Refreshments will be served in FO 2.610F 30 minutes before the talk begins.

 

 

Contact Info:
John Zweck, 972-883-6699
Questions? Email me.

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