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Efficient stochastic particle dynamics for high-dimensional simulation

Matthew West
University of Illinois at Urbana-Champaign


High-dimensional numerical simulation problems arise in diverse contexts, including in population balance models, an application that motivates our numerical algorithm design. To enable discretization in tens of dimensions, we focus on particle (meshless) methods with Markov jump process dynamics. While numerical methods for such systems have been known since the mid-1970s, efficient techniques that enable large-scale simulation are much more recent. In this talk we present advances in three key aspects. First, we show how multiscale rate functions can be efficiently simulated by applying importance-sampling ideas to tau-leaping time-discretizations. This is particularly relevant for systems with a continuum of scales from slow to fast, without clear scale separations that would enable homogenization. The second development we discuss is variable resolution in the sample-space, where non-uniform particle samplings can be used to achieve variance reduction for particular observables of the process. We show how such non-uniform or variable sampling can be driven by local error estimators, allowing adaptive resolution for the system state discretization. Finally, we present a new parallelization technique for Markov jump processes, based on particle diffusion across well-chosen network paths between processor nodes. While the Markov process naively involves dense communication, we show how sparse communication can give accurate approximations with near-linear scaling.

Thursday, May 5, 2011
2:00PM AP&M 2402