# Maria K. Cameron

### University of Maryland, Department of Mathematics

#### Summer 2023

##### ** Topic 3.** Data-driven methods and model reduction for the study of rare events in stochastic systems.

Prof. Maria Cameron (UMD, MATH)
**Prerequisites:** linear algebra, multivariable calculus, elementary probability, and some programming experience.

Many physical processes such as conformal changes in biomolecules and switches between stable modes in nonlinear oscillators are modeled using stochastic differential equations with small noise. The events of interest, the transitions between metastable states of such systems, happen rarely on the timescale of the system. As a result, their study by means of direct simulations requires extremely large runtimes. We will explore alternative approaches to the study of rare events in such systems based on model reduction and various tools originating from data science and machine learning. For example, a reduced model for an array of nonlinear oscillators with periodic forcing and small noise can be a discrete-time Markov chain, whose stochastic matrix needs to be learned from data. A reduced model for a molecular system can be learned from data by means of training a neural network to represent the original high-dimensional model in a low-dimensional space. Such a neural network is called an autoencoder.

###### Design by Michelle Cameron