Speaker: Dr. Fei Lu from Johns Hopkins University
Date and Time: Friday, October 22, 2021, 11am-12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.
Title: A statistical learning perspective of model reduction
Abstract: Stochastic closure models aim to make timely predictions with uncertainty quantified. We discuss the statistical learning framework that achieves this goal by accounting for the effects of the unresolved scales. A fundamental idea is the approximation of the discrete-time flow map for the dynamics of the resolved variables. The flow map is an infinite-dimensional functional of the history of resolved scales, as suggested by the Mori-Zwanzig formalism. Thus its inference faces the curse of dimensionality. We investigate a semi-parametric approach that derives parametric models from numerical approximations of the full model. We show that this approach leads to effective reduced models for deterministic and stochastic PDEs, such as the Kuramoto-Sivashisky equation and the viscous stochastic Burgers equations. In particular, we highlight the shift from the classical numerical methods (such as the nonlinear Galerkin method) to statistical learning, and discuss space-time reduction.