Scientific Context

The computational cost of solving PDE, for instance CFD (Navier-Stokes) and electromagnetic (Maxwell) equations, for real industrial situations, is problematic today. The use of HPC computing does not allow us to manipulate these resolution algorithms quickly enough to integrate them into digital twins useful to engineers, without making numerical compromises (for example, using a 2D resolution for a real 3D problem). These compromises historically form a set of “reduced” physical models (Reduced Order Models, or ROMs), whose construction requires an intrusive approach to large, accurate numerical models. While ROMs have made it possible to approximate the resolution of many problems, the possibility of using the most recent learning tools (kriging, neural networks, etc.) from simulation databases, but also from knowledge of boundary conditions, or even a mesh, has emerged in recent years. The field of Physics-informed Machine Learning is currently flourishing, and numerous approaches have been proposed, such as PINNs (Physics-informed Neural Networks), GNNs (Graph Neural Networks), GNO, operator-based approaches, etc. These promising trials are still examining relatively simple cases. Our ambition is to develop approaches that will really enable us to handle industrial cases that have arisen in recent years.

Content

The research school is aimed at PhD students, young researchers and more experienced researchers wishing to learn more about the subject. Courses including practical works will be given by top professors and well-known researchers from both academic and industrial worlds will give thematic conferences. Classical examples will be introduced, but point out that one of the expected gains of the research school is to be able to find one’s way through the “jungle” of approaches, and to be introduced to increasingly complex application examples. Technological choices as well as discussions on most recent approaches, as foundational models, are on the agenda. Furthermore, PhD students and young researchers who will attend will have the possibility to apply for presenting a poster.

Invited speakers

• George Kardaniakis (Brown University)
• Patrick Gallinari (SCAI)
• J. Nathan Kutz (University of Washington)
• Claire Boyer (Université Paris Saclay)
• Siddharta Mishra (ETH Zurich)
• Claire Monteleoni (INRIA & University of Colorado)
• David Greenberg (Helmhotz AI)
• Boris Bonex (Nvidia)

Practical Information

Date

16 june – 20 june 2025

Place

EDF Lab
Paris-Saclay
7 Boulevard Gaspard Monge
91120 Palaiseau

Contacts

Summer schools secretary
Régis Vizet – CEA
tel: 01 69 26 47 45
Fax: 01 69 26 70 05

Coordinators of the numerical analysis 2025 school
Christophe Millet
Bruno Raffin
Vincent Le Guen
Nicolas Bousquet
Alejandro Ribes