I started a few years ago (2018) to investigate the interplay between machine learning and physics mainly for the modeling of spatiotemporal 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: MachineLEARNing 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 spatiotemporal representations. The objective is to get space/ time resolution independent or mesh free models of the dynamics.
Tutorial on physicsaware 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 coadvisor – include several pluridisciplinary theses coadvised 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 DechelleMarquet – 2023 – Deep learning based physicalstatistics modeling of ocean dynamics
 Matthieu Kirchmeyer – 2023 – OutofDistribution Generalization in Deep Learning: Classification and Spatiotemporal Forecasting
 Yuan Yin – 2023 – PhysicsAware Deep Learning and Dynamical Systems : Hybrid Modeling and Generalization
 Victoriya Kashtanova – 2023 – Learning cardiac electrophysiology dynamics with PDEbased physiological constraints for datadriven personalised predictions
 Léon Migus – 2023 – Deep neural networks and partial differential equations