Neural Network-based Inverse problems for Maxwell PDE’s: applications to electromagnetic source[...]

European Commission; France; Sur place; EUR 30 000 - 40 000; Plein temps

Résumé du poste

Une université de Normandie recherche un postdoctorant pour un projet innovant sur l'utilisation de l'intelligence artificielle dans la recherche scientifique. Le candidat développera des méthodes hybrides pour résoudre des problèmes complexes en électromagnétisme, en mettant l'accent sur l'interdisciplinarité et l'innovation. Ce poste offre une opportunité unique de contribuer à des recherches de pointe dans un environnement dynamique.

Qualifications

• Doit détenir un PhD dans un domaine pertinent.
• Expérience antérieure en apprentissage automatique requise.
• Goût pour la recherche interdisciplinaire apprécié.

Responsabilités

• Développer des méthodes hybrides basées sur des réseaux de neurones pour résoudre des problèmes d'inverse en électromagnétisme.
• Étudier les problèmes d'un point de vue théorique et computationnel.

Connaissances

Apprentissage automatique

Recherche interdisciplinaire

Compétences computationnelles

Formation

PhD en physique, mathématiques ou informatique

Description du poste

Organisation/Company Normandie Université Department Engineering and Computer Science dept. Research Field Computer science » Modelling tools Physics » Electromagnetism Researcher Profile Recognised Researcher (R2) Positions Postdoc Positions Country France Application Deadline 30 Sep 2025 - 00:00 (Europe/Paris) Type of Contract Temporary Job Status Full-time Offer Starting Date 1 Oct 2025 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

Offer Description

Scientific environment:

The postdoctoral project is part of the new CAI4Science(AI for Science in Caen) interdisciplinary initiative within the University of Caen Normandy. CAI4Science is an ambitious research project that aims to harness the transformative potential of artificial intelligence (AI) to accelerate scientific discovery across various fields. The project brings together the expertise of researchers in computer science, mathematics, physics, chemistry and material sciences, affiliated to four major CNRS laboratories at the University of Caen Normandie (CIMAP, CRISMAT, LPC, and GREYC). The goal is to develop the potential of advanced AI/machine learning methods to solve challenging problems in physics and material sciences.

Scientific context:

Maxwell’s partial differential equations (PDEs) form the foundation of electromagnetism. Our interest lies in solving inverse problems associated with these PDEs, and more precisely in recovering magnetic sources based on observed electromagnetic field data [1]. These problems are central to applications ranging from nanoparticle functionalization detection to magnetometry applications in medicine (e.g., magnetocardiography, magnetoencephalography), non-destructive testing, geomagnetism, magnetic source localization and autonomous vehicles. Such problems are known to be notoriously ill-posed and difficult to solve, raising both theoretical and computational challenges.

While variational model-based methods and regularization theory have been the driving paradigm for solving inverse problems for decades, neural network (NN)-based hybrid methods have witnessed a spectacular development in recent years boosted by the advent of deep learning. Hybrid (physics-informed) methods attempt to take the best of both worlds: the model-based one by taking into account the underlying physics, and the NN data-driven one which, roughly speaking, parametrize the inversion process (or parts of it) using neural networks. Such methods include the deep inverse prior, plus-and-play, unrolling, and others. Generative diffusion-based models have also been recently applied to solve inverse problems via appropriate Bayesian formulations [2,3].

Scientific objectives:

Despite the wealth of existing approaches, these cannot be used off-the-shelf to solve complex inverse problems, such as the ones we target here. In a preliminary work in our group, we have adapted the PINNs methdology [5] to the setting of magnetic dipole localization. Figure 1 compares the results obtained using the PINNs methdology and the theoretical solution whose closed-form was known in this experiment.

The main objective of this post-doc is to go far beyond this preliminary work develop novel NN-based hybrid methods to solve the electromagnetic source localization inverse problem associated to the Maxwell equations. The goal is to study this problem both from the theoretical perspective (existence, uniqueness, training dynamics and implicit regularization theory, neural networks architecture, stability), and the computational one (discretization, error bounds, implementation, etc.). A particular emphasis will also be put on uncertainty quantification of the recovered sources.

• C.Dolabdjian, C.Cordier, Analysis by systemic approach of magnetic dipole source location performances by using an IoT software gradiometer head, IEEE Sensors Journal, 22(8), 7709-7716(2022) – DOI : 10.1109/JSEN.2022.3156858.
• Daras, G.; Chung, H.; Lai, C.-H.; Mitsufuji, Y.; Ye, J. C.; Milanfar, P.; Dimakis, A. G.; Delbracio, M. A Survey on Diffusion Models for Inverse Problems. https://arxiv.org/abs/2410.00083.
• P. Leveque, S. Besnard, C. Dolabdjian, F. Jurie, How Physics-Informed Neural Networks (PINNs) could be applied in magnetic source localization and characterization, EMSA’24, Kosice, Slovakia(2024).
• M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comp. Phys., 378:686–707, 2019.

To apply:

Please submit the following documents via email:

• A CV including a list of publications.
• A cover letter outlining your research statement, background, and motivation for applying.
• A list of references to be contacted.

Where to apply

E-mail [e-mail]

Requirements

Research Field Computer science » Modelling tools Education Level PhD or equivalent

Research Field Physics » Electromagnetism Education Level PhD or equivalent

Skills/Qualifications

The candidate is required to hold a PhD in either physics, mathematics, computer science or related fields. The candidate should also have a strong computational background and previous experience in machine learning. A taste for interdisciplinary research is a plus.