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Du 1 septembre 2021 au 31 août 2024

Starting fall 2021
PSL, Paris
Conatct :

We propose a PhD position to explore potentially different research tracks at the crossroad of Physics and machine learning: (i) Noisy, scarce and partial observations, (ii) Training algorithm to enforce physical properties, (iii) Physical applications.

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Alexandre Allauzen1,Sergio Chibbaro2
LAMSADE, Dauphine Université, ESPCI, PSL
Institut d’Alembert Sorbonne Université , F-75005 Paris, France alexandre.allauzen@dauphine.psl.eu sergio.chibbaro@sorbonne-universite.fr

The position will start as soon as possible, and the subject is under construction. It will be funded by the ANR project called SPEED. The project is in collaboration with the lab LISN at Orsay where many other students work on the same subject, and frequent discussions are to be expected.
Context: The interaction between machine learning and Physics has transformed the methodology in many research areas. Simulations of complex physical systems provide an illustration of such recent development. While computer simulations are invaluable tools for scientific discovery and forecasting systems, the cost of accurate simulations limits in many cases their applicability and the capacity to explore a wide range of physical parameters or to quantify uncertainty in the prediction. In the last decades, data-driven approaches have offered an efficient workaround. For instance a deep-learning model can be learned to emulate the physical model. Then, its computational efficiency makes it a proxy integrated in a forecasting system or a control loop. Another example is the recent link between deep architectures, such as ResNets, and ODEs. This promising research line proposes to analyze and improve DNNs by taking advantage of the long research history in numerical analysis. Depending on the skills of the candidate, different tracks can be explored.

Phd topics Within this project, we propose a PhD position to explore potentially different research tracks at the crossroad of Physics and machine learning:

• Noisy, scarce and partial observations. In modern machine learning, the cornerstone is to let the model learn its own representation of the process from data observation. In the case of complex physical systems, data comes from sensors being partial, noisy and scarce. While these challenging conditions are new in the machine learning domain, we can we can leverage some important properties like symmetries and invariances to address these challengesnin the context of Physics.

  • Training algorithm to enforce physical properties. The physical phenomena at hand are either simulated from PDE, or real observations, but the underlying physical model is assumed to follow to be governed by a PDE. Therefore, the link between solvers and training DNNs can be leveraged to some extent. We plan to explore a tighter interaction between the numerical methods used to solve the PDEs, the physical process under consideration and the training algorithm for DNNs.

  • Physical applications. The algorithm developments should be assessed in interesting physical situations. The accent is put here on chaotic dynamical systems as a paradigm of complex systems, rather than on optimisation problems. It would be key to show which are the bounds to a data-driven approach and how to optimise it, both in low and, more importantly, high dimensional systems. In particular, leaving aside the pure data-driven approach, it would be important to find out whether a physical-informed approach can overcome some of the difficulties presented by a blind use of machine-learning. Systems of increasing difficulties will be considered, possibly starting from the Lorenz63 one, but rapidly going through full PDE models, like the Kuramoto-Sivashinsky and the Kardar-Parisi- Zhang. The latter is rich physical model at the basis of many applications in non-equilibrium statistical physics, and appears particularly relevant to get new insights. Indeed, it includes a noise term in the model, and the issue of stochastic noise in machine learning appears less understood.