Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. To achieve the efficiency, dimension reduction is often required in both space and time. In this talk, I will talk about our recent work on both spatial and temporal reductions. For spatial dimension reduction, the Mori-Zwanzig formalism is applied to derive equations for the evolution of linear observables of the Langevin dynamics for both overdamped and general cases. For temporal dimension reduction, we introduce a framework to construct inference-based schemes adaptive to large time-steps (ISALT) from data, achieving a reduction in time by several orders of magnitudes while preserving structures of the system.
This is a joint work with Dr. Thomas Hudson from the University of Warwick, UK; Dr. Fei Lu from the Johns Hopkins University and Dr Xiaofeng Felix Ye from SUNY at Albany, and Dr. Molei Tao from Georgia Institute of Technology.