Registration in Bounded Domains for Model Reduction of Parametric Conservation Laws

Résumé

In this talk, I review recent efforts on the development of registration methods for parametric model order reduction (MOR), with 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 enhance 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 show the potential of the method.

Tommaso Taddei

Tommaso Taddei is an Associate Professor of Numerical Analysis at Sapienza University of Rome; he is a faculty member of the group of Numerical Analysis and Scientific Computing in the Department of Mathematics at Sapienza, and he is also affiliated to the joint Inria-Onera team MONHADE. His research focuses on the development, the analysis, and the 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 the group of Professor Yvon Maday at Laboratoire Jacques-Louis Lions at Sorbonne University, and a PhD student in the group of Professor Anthony Patera in the Department of Mechanical Engineering at MIT.