Registration in Bounded Domains for Model Reduction of Parametric Conservation Laws

Abstract

In this talk, I review recent efforts in the development of registration methods for parametric model order reduction (MOR), with an emphasis on advection-dominated flows. In computer vision and pattern recognition, registration refers to the process of finding a parametric transformation that aligns two datasets; in model order reduction, registration methods seek a parametric bijection that tracks coherent structures (e.g., shocks, shear layers) of the solution field. The ultimate goal is to improve the performance of traditional linear compression methods (e.g., POD) and mesh adaptation techniques for the mapped solution field.

We discuss the application of registration techniques to model reduction. First, we illustrate the combination of registration with projection-based reduced-order models and parametric mesh adaptation. Second, we discuss the application of registration to nonlinear interpolation. We present numerical results for two- and three-dimensional parametric compressible flows to demonstrate the method’s potential.

Tommaso Taddei

Tommaso Taddei is an associate professor of numerical analysis at Sapienza University of Rome; he is a faculty member of the Numerical Analysis and Scientific Computing group in the Department of Mathematics at Sapienza, and he is also affiliated with the joint Inria-Onera team MONHADE. His research focuses on the development, analysis, and implementation of model order reduction and data assimilation methods, with applications in continuum fluid and solid mechanics. Before joining Sapienza, he was a permanent researcher ( chargé de recherche ) at Inria Bordeaux, a postdoctoral associate in Professor Yvon Maday’s group at the Laboratoire Jacques-Louis Lions at Sorbonne University, and a Ph.D. student in Professor Anthony Patera’s group in the Department of Mechanical Engineering at MIT.