Supervision : Patrick GALLINARI

Modeling Physical Processes with Deep Learning: A Dynamical Systems Approach

Deep Learning has emerged as a predominant tool for AI, and has already many applications in fields where data is abundant and access to prior knowledge is difficult. This is not necessarily the case for natural sciences, and in particular, for physical processes. Indeed, these have been the object of study since centuries, a vast amount of knowledge has been acquired, and elaborate algorithms and methods have been developed. Thus, this thesis has two main objectives. The first considers the study of the role that deep learning has to play in this vast ecosystem of knowledge, theory and tools. We will attempt to answer this general question through a concrete problem: the modelling complex physical processes, leveraging deep learning methods in order to make up for lacking prior knowledge. The second objective is somewhat its dual: it focuses on how perspectives, insights and tools from the field of study of physical processes and dynamical systems can be applied in the context of deep learning, in order to gain a better understanding and develop novel algorithms.

2019-2022 Publications

• 2022
  • Y. Yin, V. Le Guen, J. Donà, E. De Bézenac, I. Ayed, N. Thome, P. Gallinari : “Augmenting physical models with deep networks for complex dynamics forecasting”, Journal of Statistical Mechanics: Theory and Experiment, vol. 2021 (12), pp. 124012, (IOP Publishing) (2022)
• 2021
  • E. De Bezenac : “Modeling Physical Processes with Deep Learning: A Dynamical Systems Approach”, thesis, defence 10/21/2021, supervision Gallinari, Patrick (2021)
  • M. Kirchmeyer, A. Rakotomamonjy, E. De Bézenac, P. Gallinari : “Mapping conditional distributions for domain adaptation under generalized target shift”, (2021)
  • J.‑Y. Franceschi, E. De Bézenac, I. Ayed, M. Chen, S. Lamprier, P. Gallinari : “A Neural Tangent Kernel Perspective of GANs”, (2021)
  • Y. Yin, I. Ayed, E. De Bézenac, N. Baskiotis, P. Gallinari : “LEADS: Learning Dynamical Systems that Generalize Across Environments”, (2021)
• 2020
  • S. Karkar, I. Ayed, E. De Bézenac, P. Gallinari : “A Principle of Least Action for the Training of Neural Networks”, ECML PKDD, Ghent, Belgium (2020)
• 2019
  • E. De Bézenac, A. Pajot, P. Gallinari : “Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge”, (2019)
  • I. Ayed, E. De Bézenac, A. Pajot, J. Brajard, P. Gallinari : “Learning Dynamical Systems from Partial Observations”, (2019)