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Laboratoire/Entreprise : Sorbonne Universite – ISIR – Institut des Systèmes
Durée : 36 mois
Contact : patrick.gallinari@sorbonne-universite.fr
Date limite de publication : 2023-12-15

Contexte :
Physics-aware deep learning is an emerging research field aiming at investigating the potential of AI methods to advance scientific research for the modeling of complex natural phenomena. This research topic investigates how to leverage prior knowledge of first principles (physics) together with the ability of machine learning at extracting information from data. This is a fast-growing field with the potential to boost scientific progress and to change the way we develop research in a whole range of scientific domains. An area where this idea raises high hopes is the modeling of complex dynamics characterizing natural phenomena occurring in domains as diverse as climate science, earth science, biology, fluid dynamics, etc.

Sujet :
The objective of the PhD project is the development of Physics-aware deep learning methods for the modeling of complex spatio-temporal dynamics. The direct application of state-of-the-art deep learning (DL) methods for modeling and solving physical dynamics occurring in nature is limited by the complexity of the underlying phenomena, the need for large amounts of data and their inability to learn physically consistent laws. This has motivated the recent exploration of physics-aware methods incorporating prior physical knowledge. Although promising and rapidly developing, this research field faces several challenges. For this PhD project we will address two main challenges, namely the construction of hybrid models for integrating physics with DL and generalization issues which condition the usability of DL for physics.

— Integrating DL and physics for spatio-temporal dynamics forecasting and solving PDEs

In physics and many related fields, partial differential equations (PDEs) are the main tool for modeling and characterizing the dynamics underlying complex phenomena. Combining PDE models with ML is a natural idea when building physics-aware DL models and it is one of the key challenges in the field. This has been explored for two main directions: (i) augmenting low resolution solvers with ML in order to reach the accuracy of high-fidelity models at a reduced computational cost, and (ii) complementing incomplete physical models with ML by integrating observation data through machine learning. A first direction of the PhD will then be to investigate hybrid physics-DL models using the recently proposed framework of neural operators. The latter opens the possibility of combining and learning multiple spatio-temporal scales within a unified formalism, a challenge in DL.

— Domain generalization for deep learning based dynamical models

Explicit physical models come with guarantees and can be used in any context (also called domain or environment) where the model is valid. These models reflect explicit causality relations between the different variables involved in the model. This is not the case for DL: statistical models learn correlations from sample observations, their validity is usually limited to the context of the training domain. This is a critical issue for the adoption of ML for modeling the physical world. In relation with the construction of hybrid models as described above, one will investigate this issue along two main directions. The first one is a purely data-based approach and exploits ideas from learning from multiple environments through task decomposition. The second one, takes a dual perspective, relying on prior physical knowledge of the system equations and directly targets the problem of solving parametric PDEs, exploiting ideas from meta-learning.

Profil du candidat :
Computer science or applied mathematics. Good programming skills.

Formation et compétences requises :
Master degree in computer science or applied mathematics, Engineering school. Background and experience in machine learning.

Adresse d’emploi :
Sorbonne Université (S.U.), Pierre et Marie Campus in the center of Paris. The candidate will integrate the MLIA team (Machine Learning and Deep Learning for Information Access) at ISIR (Institut des Systèmes Intelligents et de Robotique).

Document attaché : 202306130923_2023-04-PhD-Description-Physics-Aware-Deep-Learning.pdf