Description

This thesis aims to reconstruct the three-dimensional current density in electrochemical systems (lithium-ion batteries and fuel cells) from magnetic field measurements. The objective is to develop a non-invasive diagnostic method based on solving an inverse problem, incorporating physical constraints and regularization techniques. The approach will combine electromagnetic modeling and machine learning methods. The work will rely on both simulated and experimental data, obtained in particular using AMR/TMR sensor arrays. A measurement prototype for fuel cells is currently under development and will be used for validation. Applications include fault detection and analysis of internal operation. The topic lies at the interface between physics, scientific computing, and machine learning.

Skills required

The candidate should hold a Master’s degree (or equivalent) in applied mathematics or engineering, with skills in: - Control systems, signal processing, numerical methods - Physics (electromagnetism), modeling of dynamical systems - Scientific programming and machine learning An interest in inverse problems and machine learning will be considered an asset.

Bibliography

[1] 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. Journal of Computational physics, 378 :686–707, 2019.
[2] S. E. Crawford et al., « Quantum sensing for emerging energy technologies », Nat. Rev. Clean Technol., vol. 1, no 12, p. 861 876, oct. 2025, doi: 10.1038/s44359-025-00112-7.
[3] H. Zhao et al., « Non-destructive detection techniques for lithium-ion batteries based on magnetic field characteristics-A model-based study », J. Power Sources, vol. 604, p. 234511, juin 2024, doi: 10.1016/j.jpowsour.2024.234511.
[4] F. Bertrand, T. Jager, A. Boness, W. Fourcault, G.l Le Gal, et al.. A 4He vector zero-field optically pumped magnetometer operated in the Earth-field. Review of Scientific Instruments, 2021, Volume 92, Issue 10, October 2021, pp.105005, doi: 10.1063/5.0062791.
[5] R. Lopez-Ferber, S. Leirens, D. Georges, « Procédé de détermination de coordonnées dans l'espace d'une source à l'origine d'un phénomène de dispersion », Brevet EP 4 488 854 A1.
[6] M. Mendil, S. Leirens, P. Armand, C. Duchenne, “Hazardous atmospheric dispersion in urban areas: A Deep Learning approach for emergency pollution forecast”, Environmental Modelling & Software, Volume 152, 2022
[7] R. Lopez-Ferber, D. Georges, S. Leirens, “Fast Estimation of Pollution Sources in Urban Areas Using a 3D LS-RBF-FD Approach”, European Control Conference, 2024, Stockholm, Sweden.

Keywords

estimation, magnetic, physics-informed, machine learning