UQSay #80
The eightieth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 12, 2024.
2–3 PM — Claire Boyer (LMO, UPS)
A primer on physics-informed learning
Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. Practitioners often resort to physics-informed neural networks (PINNs) to solve this kind of problem. After discussing some strengths and limitations of PINNs, we prove that for linear differential priors, the problem can be formulated directly as a kernel regression task, giving a rigorous framework to analyze physics-informed ML. In particular, the physical prior can help in boosting the estimator convergence. We also propose the PIKL algorithm (PIKL for physics-informed kernel learning) as a numerical strategy to implement this kernel method.
References:
- Convergence and error analysis of PINNs, Bernoulli 2024
- Physics-informed machine learning as a kernel method, 2024
- Physics-informed kernel learning, 2024
Joint work with N. Doumèche (Sorbonne University) & G. Biau (Sorbonne University) & F. Bach (INRIA).
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.