CDS/CIMMS Seminar: Nested Stochastic Simulation Algorithm for Kinetic Monte Carlo Systems with Disparate Rates

Dr. Eric Vanden-Eijnden, Courant Institute of Mathematical Sciences. New York
eve2@cims.nyu.edu

The talk will present a new numerical algorithm for simulating continuous-time Markov chains with  multiple time-scales. This algorithm is an improvement of the traditional stochastic simulation algorithm (SSA), also known as Gillespie's algorithm. It is in the form of a nested SSA and uses an outer SSA to simulate the slow reactions with rates computed from realizations of inner SSAs that simulate the fast reactions.  The algorithm itself is quite general and seamless, and it amounts to a small  modification of the original SSA. It can be justified using averaging theorems to multi-scale continuous-time Markov chains which allow one to identify the slow variables in the system, derive effective dynamics on the slow time scale, and give error estimates for the nested SSA. The efficiency of the nested SSA will be discussed using these error estimates, and illustrated through several numerical examples.