Applied mathematics Colloquium: Dr. Xiaofeng Ye
Johns Hopkins University
Location
Online
Applied mathematics Colloquium: Dr. Xiaofeng Ye – Online Event
Date & Time
November 6, 2020, 2:00 pm – 3:00 pm
Description
Title is Nonparametric nonlinear model reduction for slow-fast SDEs near manifolds.
Abstract: Multi-timescale stochastic dynamical systems are classical problems in physical systems. In order to reduce the computational costs, it is essential to reduce the stochastic dynamics to the slow variables on the slow invariant manifold. Because usually, these slow variables are low dimensional. However, in practice, we usually don’t know which one is the slow variable from the ambient space. In this work, we propose a novel approach to automatically learn a reduced stochastic equation on the slow manifold with an associated macroscale simulator. Our algorithm uses short parallelizable microscale simulations to learn accurate drift and diffusion terms in the reduced equations, together with the ATLAS of the slow manifold. The main idea is: at the scale of the relaxation time of the fast variable, the dynamics of the fast variable reached equilibrium and is approximated by an Ornstein-Uhlenbeck process, but the dynamics of the slow variable is approximated by the constant drift and constant diffusion. We will discuss various synthetic and realistic examples, as well as results on the accuracy of the macroscale simulators that we construct.
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