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 Karniadakis (Brown University)
• Patrick Gallinari (SCAI)
• Claire Boyer (Université Paris Saclay)
• Siddharta Mishra (ETH Zurich)
• Ronan Fablet (IMT Atlantique)
• Boris Bonev (Nvidia)

Preliminary program

– Day 1: June 16
08:45-09:15: Welcome breakfast
09:15-09:30: Welcome and presentation of the school (organizers)

09:30-11:00: Patrick Gallinari (Sorbonne Université) : General introduction: From basic learning techniques to the various theories of information representation in field physics
(coffee break around 11:00)
11h30-13h : Jean-Christophe Loiseau (Arts & Métiers Institute of Technology) : System identification / operator learning I (theoretical principles

13:00-14:00: Lunch

14:00-17:00:George E. Karniadakis & Khemraj Shukla (Brown University): PINN & PIKAN & Neural Operators I (theoretical principles)

(coffee break around 15:30)

Welcome cocktail

– Day 2: June 17
09:00-09:30: Welcome coffee

09:30-12:30: George E. Karniadakis & Khemraj Shukla (Brown University): PINN & PIKAN & Neural Operators II (applications / directed works)

(coffee break around 11:00)
12:30-14:00: Lunch

14:00-17:30: Jean-Christophe Loiseau (Arts & Métiers Institute of Technology) : System identification / operator learning II (applications / directed works with PySCINDY)
(coffee break around 15:30)

Banquet

– Day 3: June 18

09:30-12:30:

09:30-11:00: Patrick Gallinari (Sorbonne Université) : Generalization in physics-based deep learning
11:30-12:30 : Claire Boyer (Université Paris Saclay): A primer on physics-informed machine learning: from PINNs to kernel methods

(coffee break around 11:00)

12:30-14:30: Lunch

14:30-17:30: Poster Session (with available rooms for discussion and working meeting)

(coffee break around 15:30)

– Day 4 : June 19
09:00-09:30: Welcome coffee

09:30-12:30: Christophe Millet & Xavier Cassagnou (CEA & ENS Paris-Saclay) From Graph Neural Networks to learning dynamic graphs

(coffee break around 11:00)
12:30-14:00: Lunch + Poster session

14:00-17:30: Applications, technology and beyond
Ronan Fablet (IMT Atlantique) : End-to-end neural data assimilation: application to ocean dynamics
Boris Bonev (Nvidia) : A principled approach to probabilistic machine-learning weather forecast at scale
Bruno Raffin (INRIA) & Alejandro Ribes (EDF): On-line training of DeepSurrogates models

(coffee break around 15:15)

– Day 5 : June 20
09:00-09:30: Welcome coffee

09:30-12:30:
Alena Shilova (INRIA) : SciML perspective on solving control problems
Michele Alessandro Bucci (Safran) : Title to come : speaker en attente de confirmation

(coffee break around 11:00)
12:30-14:00: Lunch

14:00-16:00: The future of PDE with foundation models
Siddhartha Mishra (ETH Zurich) : Foundation Models for PDEs

Practical Information

Date

16 june – 20 june 2025

Place

EDF Lab
Paris-Saclay
7 Boulevard Gaspard Monge
91120 Palaiseau

Inscription

Pour pouvoir participer, merci de remplir le formulaire d’inscription et l’envoyer avant le 15 may 2025 à Régis Vizet. –>

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