### Towards the control of multiscale stochastic systems

- Series
- Job Candidate Talk
- Time
- Thursday, January 23, 2014 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Molei Tao – Courant Institute, NYU

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.