New trends in nonlinear approximation methods for parametric systems.
Angelo Iollo and Tommaso Taddei
University of Bordeaux and Sapienza University of RomeRelevance to WCCM–ECCOMAS
The topics of the short course are related to the ones of the 2024 CEA-EDF-Inria summer school https://ecoles-cea-edf-inria.fr/en/history/ecole-analyse-numerique-2024/, which was very successful (around 50 participants).
Objectives and target groups
The aim of the short research course is to provide an introduction to nonlinear approximation methods for parametric PDEs, with focus on methods based on coordinate transformations: topics include parametric registration in bounded domains, nonlinear interpolation and connections with optimal transportation, Fokker-Planck equations and Schrödinger Bridges, projection-based model reduction. We shall also address the connection and the potential interaction between the development of nonlinear approximation methods and recent efforts in generative modeling.
Scientific and technical areas covered
- Model order reduction for parametric PDEs
- Shock-dominated flows of interest in aerodynamics
- Scientific machine learning (generative modeling, optimal transport)
Bio-sketch
Angelo Iollo is an applied mathematician working in numerical modeling, reduced-order modeling and scientific computing for fluid dynamics and aerospace applications. He is a Professor at the Institute of Mathematics of Bordeaux within the University of Bordeaux, and he also serves as the head of the MONHADE project, a common research team of Inria and Onera, where he leads and coordinates research at the intersection of continuum mechanics and scientific computing.
He is actively involved in translating applied mathematics into practical enterprise solutions. He contributed to the establishment of Optimad Engineering, a numerical engineering spin-off originating from the Politecnico di Torino, as well as Nurea, a startup spun out of Inria that provides specialized cardiovascular decision-support software.
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 (chargè 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.
