Event

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

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Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear PDE and construct a filtered ROM. This filtered ROM is low-dimensional, but is not closed (because of the PDE nonlinearity). (ii) In the second step, we use ResNet to close the filtered ROM,i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new model is built on general ideas of spatial fil and deep learning and is independent of the (restrictive) phenomenological arguments, e.g., of eddy viscosity type.
 
Speaker’s Bio: Xuping Xie received his Ph.D. in Mathematics from Virginia Tech in May 2017. His research was focused on reduced order models for nonlinear fluids with Dr. Traian Iliescu. Currently he is working on machine learning based data-driven modeling for nonlinear dynamics.

Last Updated: May 28, 2020 - 4:03 pm