Data-Driven Filtered Reduced Order Modeling for Nonlinear Systems

Thursday, March 1, 2018 - 10:00 to 11:00
Thackeray 427
Speaker Information
Traian Iliescu
Virginia Tech

Abstract or Additional Information

We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of nonlinear systems. The novel DDF-ROM framework consists of two steps:  (i) In the first step, we use ROM projection to filter the nonlinear PDE and construct a filtered ROM.  This filtered ROM is low-dimensional, but is not closed (because of the nonlinearity in the given PDE).  (ii) In the second step, we use data-driven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes.  To this end, we use a quadratic ansatz to model this interaction and close the filtered ROM.  To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz.  We emphasize that the new DDF-ROM is built on general ideas of spatial filtering and optimization and is  independent of (restrictive) phenomenological arguments.

Research Area