Math 697SC: Computational Methods for Stochastic Systems

Instructor: Professor Markos Katsoulakis, LGRT 1423G, E-mail: markos [at] math umps edu

Lectures: Tuesdays, Thursdays, 1:00PM-2:15PM, Room LGRT 1334.

Office Hours: Tuesdays, Thursdays, 12:30PM-2:00PM or by appointment.

Free Energy Computations: A Mathematical Perspective; Authors: T. Lelievre, M. Rousset, G. Stoltz; Imperial College Press, Year Published: 2010. (available electronically through the Umass Library)
Selected papers and reviews (to be assigned depending on topic)

Stochastic Simulation Algorithm (SSA) and variants: StochKit.
Codes discussed in the Textbook.
A wide selection of Stochastic Algorithms and Software primarily for biological and chemical systems, see this article.
Molecular Dynamics and Kinetic Monte Carlo Software and their parallelization from SANDIA.

This course presents some of the fundamental as well as state-of-the-art methods for the simulation of stochastic processes, with particular emphasis in high dimensional systems. Such stochastic models are ubiquitous in the applied sciences and engineering, arising in applications ranging from materials to biology to geophysics, economics and finance to name a few. The course will include a project component that will be selected and carried out in coordination between the instructor and the project participant(s). Material includes: 1. Introduction to Monte Carlo methods, 2. Markov Chain and Kinetic Monte Carlo methods, 3. Numerical methods for Stochastic Differential Equations, 4. Polynomial Chaos and model Reduction methods for Stochastic Partial Differential Equations, 5. Multi-level and parallelization techniques for high-dimensional stochastic systems, 6. Hybrid, multi-physics systems.
Prerequisites: Knowledge of basic concepts in probability theory (Math/Stat 515), Differential Equations (Math 532 or 534) and some experience with programming.

Fall Semester 2012-2013.