Title:

COARSE – GRAINING OF STOCHASTIC SYSTEM

Abstract:

Stochastic differential equation (SDE) models are essential for capturing the dynamics of diverse real-world phenomena, such as the intricate flow and transport processes in complex porous media. To simulate and to predict the behavior of SDE models, stable numerical integration algorithms are needed, in particular for long-time simulations. In this work, we derived a family of one-dimensional benchmark problems to evaluate the stability of numerical schemes for SDEs. We used this benchmark to present an analysis of the asymptotic stability of four explicit numerical schemes used for simulating SDEs across a range of convergence orders. Meanwhile, we demonstrate the utility of our results in the context of a more realistic setting of particle diffusion in porous media, where the drift and diffusion coefficients are both nonlinear. We observed that lower-order schemes tend to preserve asymptotic statistical accuracy better than higher-order schemes, a trend which persists in testing of a realistic nonlinear benchmark problem.

This is a joint work with Dr Thomas Hudson from the University of Warwick, UK.

Bio:

Dr Xingjie Helen Li is an Associate Professor at UNC Charlotte. Her research focuses on multiscale modeling and structure-preserving numerical schemes, with applications in materials science and stochastic dynamics. Her work has been supported by multiple NSF grants, including a NSF CAREER award.