# Graduate Student / Postdoc Seminar

#### Learning and Fast Simulation of Intrinsically Low-Dimensional Stochastic Dynamical Systems in High Dimensions

**Speaker:**
Miles Crosskey, Duke University

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, January 31, 2014, 1 p.m.

**Synopsis:**

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales and high-dimensionality can make simulations computationally very expensive. The size of time steps are dictated by the micro scale properties, while interesting behavior often occurs on the macro scale. This forces us to take many time steps in order to learn about the macro scale behavior. In this talk I will present a general framework for using micro scale simulations to automatically learn accurate macro scale models of certain SDEs. This method is particularly efficient when the SDE and the macro scale has low-intrinsic dimension, i.e. a small number of effective degrees of freedom. The learned macro scale model can then be used for fast computation and storage of long simulations. I will discuss various examples, both low- and high-dimensional, as well as results about the accuracy of the fast simulators we construct, and its dependency on the number of short paths of the original simulator available to the learning algorithm.