연사: 이형천 교수님/ 아주대학교 수학과
When: Feb. 13. 2020 (Thurs), 15:00--16:15.
where: Building 110, Room N.103

Title of talk : REDUCED ORDER BASIS METHODS FOR NON-LINEAR PDES USING DEEP NEUURAL NETWORK


Abstract : Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models(ROMs) for ealistic nonlinear systems, which generally require drastic ROM mode truncations. A data-driven reduced order model (DD-ROM) framework for the numerical simulation of Navier-Stokes equations is considered. The DD-ROM framework consists of two steps: (i) In the first step, we use Galerkin projection ROM (GP-ROM). This GP-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 GP-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 GP-ROM. To find the new coefficients in the closed ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. We emphasize that the DD-ROM is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments.
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