I started a few years ago (2018) to investigate the interplay between machine learning and physics mainly for the modeling of spatio-temporal dynamics. I am collaborating on this general topic with colleagues in geophysics, numerical analysis, fluid dynamics and health science..
I was awarded an AI Chair in 2019 – a national program from France AI strategy. The project is entitled « DL4CLIM: Deep Learning for Physical Processes ». The program will run until 2026. It is managed by french ANR, you will find the announcement page on the ANR site here.
I started this topic through a collaboration with physicist colleagues at LOCEAN labs at Sorbonne university. Since that I developed different collaborations, including colleagues from INRIA Paris (INRIA/Ange) and Sophia (INRIA/Epione) for the DeepNum project, focused on the numerical analysis of ML solveurs, Paola Cinella from d’Alembert lab. at Sorbonne Universty on the recently launched « LearnFluidS project: Machine-LEARNing for FLUID Simulations ».
In the MLIA team, we have been mainly exploring the following issues:
- How to incorporate prior physical knowledge in machine learning models
How to leverage both prior physical background on a phenomenon and information extracted from data? How can ML models come as a complement to physical ones?
- Domain generalization
When physical models are valid on whole domains, e.g. whole oceans, ML models do not generalize outside their training domain. When trained on physical data they do not capture the underlying laws of nature and do not generalize to other contexts (space or time). This is a major limitation of data based approaches to physics.
- Operator learning
Learning mappings between function spaces, leading to continuous spatio-temporal representations. The objective is to get space/ time resolution independent or mesh free models of the dynamics.
Tutorial on physics-aware deep learning
- Here is a recent tutorial at ECML 2023
Recent publications related to the topic of the chair at MLIA
- Conferences – to come – you can have a look at DPLP
- PhD Manuscripts and Theses for which I served as an advisor or co-advisor – include several pluri-disciplinary theses co-advised with colleagues in applied mathematics, climate, and fluid dynamics.
- Arthur Pajot -2019- Incorporating physical knowledge into deep neural network
- Emmanuel de Bezenac – 2021- Modeling Physical Processes with Deep Learning: A Dynamical Systems Approach
- Jérémie Donà – 2022 – Statistical Learning of Physical Dynamics
- Ibrahim Ayed – 2022 –Neural Models for Learning Real World Dynamics and the Neural Dynamics of Learning
- Marie Dechelle-Marquet – 2023 – Deep learning based physical-statistics modeling of ocean dynamics
- Matthieu Kirchmeyer – 2023 – Out-of-Distribution Generalization in Deep Learning: Classification and Spatiotemporal Forecasting
- Yuan Yin – 2023 – Physics-Aware Deep Learning and Dynamical Systems : Hybrid Modeling and Generalization
- Victoriya Kashtanova – 2023 – Learning cardiac electrophysiology dynamics with PDE-based physiological constraints for data-driven personalised predictions
- Léon Migus – 2023 – Deep neural networks and partial differential equations