Research
My research focuses on kinetic equations and fluid equations. I am interested both in the mathematical analysis of such equations and in their numerical discretisation.
On the analysis side, the questions that interest me are the well-posedness of these models, the long-time behaviour of their solutions, and the stability or instability of their equilibria.
On the numerical side, I work on the design and the analysis of structure-preserving schemes that reproduce the properties of the continuous model at the discrete level: positivity, conservation of invariants, and bounds on quantities that must remain in a given range.
Recently, I have been interested in numerical schemes that remain efficient in high dimension. In particular, I am working on methods that couple classical numerical methods with neural networks, and on their application to gyrokinetic models.
Papers and preprints
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A neural characteristic mapping method: Lagrangian PINNs based on flow maps for transport-dominated problems - with Martin Campos Pinto, Emmanuel Franck, Philipp Krah and Victor Michel-Dansac. Preprint October 2026. arXiv:2610.12395.
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A neural delta-f particle-in-cell method: evolving the background with learned backward flows — with Martin Campos Pinto, Emmanuel Franck and Victor Michel-Dansac. Preprint, June 2026. arXiv:2606.30622, HAL version.
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Landau damping in mixed hyperbolic-kinetic systems and thick sprays — with Dongfen Bian, Bruno Després and Emmanuel Grenier. Kinetic and Related Models, 2026, 23: 91–103. doi: 10.3934/krm.2026015. arXiv:2505.02295.
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Construction, analysis and implementation of two nodal finite volume schemes for the \(P_N\) model for particle transport in 2D — with Christophe Buet and Stéphane Del Pino. SMAI Journal of Computational Mathematics, Volume 11 (2025), pp. 39–84. doi: 10.5802/smai-jcm.119. HAL version.
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Analog of Linear Landau Damping in a coupled Vlasov–Euler system for thick sprays — with Bruno Després and Christophe Buet. Communications in Mathematical Sciences, 23: 235–258, 2025. HAL version.
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Local-in-time existence of strong solutions to an averaged thick sprays model — with Bruno Després and Christophe Buet. Kinetic and Related Models, 17(4): 606–633, 2024. HAL version.
Proceedings
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Investigation on the stability in a thick spray model. ESAIM: Proceedings and Surveys, 2024. HAL version.
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A coupled Semi-Lagrangian/Finite Volume scheme to deal with the close-packing limit in thick sprays — with Bruno Després and Christophe Buet. 33rd International Symposium on Rarefied Gas Dynamics — Proceedings, 2024. HAL version.
Talks
- July 2026 — Workshop Fluid Dynamics, Singularities, and AI-Driven Discovery, Speinshart, Germany.
- July 2026 — WCCM–ECCOMAS 2026, Munich, Germany.
- June 2026 — CANUM 2026, Saint-Jacut-de-la-Mer, France.
- March 2026 — SIAM Conference on Parallel Processing for Scientific Computing, Berlin, Germany.
- January 2026 — Journées Jeunes EDPistes 2026, Université Paris-Dauphine, France.
- May 2025 — SMAI 2025, Carcans-Maubuisson, France.
- June 2024 — NMPP Seminar, Max Planck Institute for Plasma Physics, Garching, Germany.
- June 2024 — RGD 2024, Göttingen, Germany.
- May 2024 — CANUM 2024, Le Bois-Plage-en-Ré, France.
- November 2023 — Numkin 2023, Max Planck Institute for Plasma Physics, Garching, Germany.
- November 2023 — PhD students’ seminar, Sorbonne Université, Paris, France.
- September 2023 — Conference for Young Researchers in Mathematics and Applications 2023, Gif-sur-Yvette, France.
- May 2023 — SMAI 2023, Pointe-à-Pitre, Guadeloupe.
- December 2022 — Workshop Kinetic and Hyperbolic Equations: Modeling, Analysis and Numerics, Institut de Mathématiques de Toulouse, France.
- June 2022 — CANUM 2022, Évian-les-Bains, France (poster).
PhD thesis
I defended my thesis, Mathematical and numerical study of thick spray models, on 22 January 2025. The manuscript is available here. I did my PhD at CEA in Bruyères-le-Châtel and at the Laboratoire Jacques-Louis Lions (Sorbonne Université) in Paris, under the supervision of Bruno Després (Sorbonne Université) and Christophe Buet (CEA).