### Mathematics Colloquium - Friday October 27th

#### Efficient sampling of stochastic nonlinear wave equations using low-dimensional reductions

- 10-17-2017
- By Melissa R Rubinchuk

**Efficient sampling of stochastic nonlinear wave equations using low-dimensional reductions**

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Professor Richard O. Moore

Department of Mathematical Sciences

New Jersey Institute of Technology

Friday, October 27th, 4:30 PM

Kalkin 001

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**Abstract: **

The ability to compute probabilities of rare events is of critical importance in several physical settings, ranging from chemical reactions to magnetic memory devices. Importance sampling using closed- or open-loop feedback based on maximum likelihood paths has been demonstrated to improve the efficiency of Monte Carlo estimation of such probabilities by several orders of magnitude, even when the maximum likelihood paths are determined from an approximate model of low dimension. We demonstrate this approach using examples taken from fiber-optic communications, mode-locked lasers, and magnetoresistive memory.

We show how careful observation of the biased dynamics can suggest improvements to the low-dimensional model that can, in turn, be fed back into new biased simulations of the full model.