Post-Doctorant F/H Generative model to enhanced optimal control of PDE and inverse problem

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Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Assignment

We are interested in addressing a broad class of optimal control problems associated with PDEs, including inverse wave problems and shape optimization. Typically, solving each control problem requires a computationally expensive gradient-based algorithm, which involves solving both the PDE and its adjoint. In this project, our goal is to leverage previously solved control problems or prior knowledge about the solution to accelerate the resolution of new control problems and enhance accuracy.
We propose to explore an approach [1,5,6] that involves approximating the distribution of relevant controls (obtained, for example, from past solutions) using a generative diffusion model. This distribution is then sampled and coupled with gradient descent to efficiently compute a solution for a new control problem. A preliminary result for PDEs was presented in [2], and we propose extending this to a slightly different class of generative models [7]. These models involve a costly sampling process that could be accelerated using techniques from [9].
Depending on the candidate's interests, we may also seek to demonstrate the advantages of this approach on relatively simple PDE control problems [8]. In the second phase, we plan to extend this methodology to shape optimization problems, with a particular emphasis on obstacle identification. For this, we propose employing generative models for shapes [3,4], where the shape is represented by a neural network. Throughout the project, a strong emphasis will be placed on computational efficiency.
 
Practical information: The post-doctorate will last 18 months.  The post-doc will take place at University of Strasbourg, within the Mathematics laboratory (downtown campus). The campus provides a very nice working environment with an excellent cafeteria.
 
Supervisors: E. Franck, L. Navoret, V. Michel Dansac (INRIA and IRMA), Y. Privat  (Mines Nancy and INRIA)
Collaborators: J. Digne (CNRS and Université Lyon 1), B. Geshkovski (INRIA and LJLL Paris), J. Aghili (INRIA and IRMA ?)

Skills

Research profil: The candidate must have a PhD in applied mathematics. This could be an EDP profile with knowledge of ML or an ML profile with knowledge of EDP. A good knowledge of Python programming is important.

Benefits package

  • Restauration subventionnée
  • Transports publics remboursés partiellement
  • Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
  • Possibilité de télétravail (après 6 mois d'ancienneté) et aménagement du temps de travail
  • Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
  • Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria)
  • Accès à la formation professionnelle
  • Sécurité sociale

Remuneration

2788 € gross/month