Colloque - Tommaso Taddei : Registration in Bounded Domains for Model Reduction of Parametric Conservation Laws

Yvon Maday Chaire Informatique et sciences numériques Collège de France Année 2025-2026 Colloque : Aspects mathématiques et appliqués des méthodes de réduction de complexité - Tommaso Taddei : Registration in Bounded Domains for Model Reduction of Parametric Conservation Laws Tommaso Taddei Associate Professor of Numerical Analysis, Department of Mathematics Guido Castelnuovo, Sapienza University of Rome, Italy 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.