Research

Research interests

Over the past years, my activity has mainly focused on the following four themes:

Data approximation In data approximation, acquiring high-precision data generates large volumes of data in both medicine and geosciences. Having acquired strong expertise in this area since my PhD thesis (!), I continue developing new models with collaborators on this topic (especially with Dominique Apprato and Carole Le Guyader), for instance, we have developed mathematical models to simulate large-scale real-world problems: for example, high-resolution ocean surface approximation (from bathymetry data) which notably allows precise modeling of the evolution of coastal areas (under the assumption of sea-level rise), or modeling tsunamis and other large-scale phenomena. Similarly, I have developed methods for data approximation from partial data, rapidly varying data, bathymetry data, geophysical data or discontinuous data (with Dimitri Komatitsch). In all this work, the problems reduce to minimization in Sobolev spaces; existence and uniqueness of a solution are studied, and discretization in finite element-type spaces is also presented. These works have been applied and validated on real data. The methods have been generalized to vector fields (PEPS of Labex AMIES with ENGIE Green - La Compagnie du vent, with Philippe Alexandre and Carole Le Guyader-), then (with different kind of inputs) with Siemens Gamesa Renewable Energy (ongoing work since 2017) as part of major projects (2021/2025 recovery plan on a project worth nearly €1M in total, as well as M2NUM project (Region and Europe) carried by LMI/INSA Rouen, also other projects like WAKE OP and M2SiNum...) and partnerships with industrial partners (including TotalEnergies, IFPEN, Dassault Systemes...), working especially with Antoine Tonnoir, Carole Le Guyader, Zoé Lambert, Norbert Warncke (SGRE), Ioana Ciotir and Nathan Rouxelin. We have also developed a method to handle much more complex data (LIDAR), this is work done as part of a contract with Siemens-Gamesa (initially with C. Le Guyader and T. Ternon), and this research axis is also part of an I-DEMO Scale Op project selected for 2024/28. A postdoc (Theau Cousin) has been recruited for 4 years (2024/28) on this €3.9M project. I also worked on data approximation with Dimitri Komatitsch. We also work on marine current approximation (Monique Chyba of the University of Hawai'i at Manoa, and H. Barucq). In approximation (RBF), I also worked with Pedro Gonzalez-Casanova and Daniel Cervantes, belonging to RBF UNAM team. Lots of these works appear in the [BOOK] by Christian Gout, Zoé Lambert, and Dominique Apprato]). On this approximation topic, I also organized many international conferences : Curves and Surfaces two times (with Marie-Laurence Mazure, Albert Cohen, Olivier Gibaru, Tom Lyche, Larry Shumaker, Jean Daniel Boissonnat, Patrick Chenin) and Multivariate Approximation; Theory and Applications (2 times in Cancun, Mexico, Poster) with P. Gonzalez-Casanova, Leonardo Traversoni, Mira Bozzini and Christophe Rabut, and also A French-Mexican conference SMM-SMAI in Villahermosa (Mexico, Poster).

Mathematical modeling and numerical simulation (imaging, energy, coastal morphodynamics...);

Velocity model and non-aligned mesh. On this research theme, I also wish to highlight two projects for which I am responsible for INSA (TeleDETact and DEPHY3GEO projects, Region Normandie and Europe) regarding drone-based remote sensing of coastal cliffs and coastal morphodynamics. For this purpose, a high-resolution thermographic camera (LWIR) mounted n a drone is used to obtain data of cliffs in coastal areas: the goal of this project was to implement observation tools to monitor coastal erosion, understand all associated phenomena, and ultimately provide initial elements of quantification. These works have been developed with CEREMA (Cyrille Fauchard and Raphael Antoine), and wity Antoine Tonnoir and Carole Le Guyader at INSA.

Finally, I highlight one ongoing thesis on this topic with Augustin Leclerc [Normandy Region funding, co-supervised with Hélène Barucq and Antoine Tonnoir on numerical modeling and simulation of electromagnetic wave propagation in offshore cables: applications to environmental impact on the marine ecosystem] and one recently defended thesis with Théau Cousin (CIFRE thesis defended in March 2024, with Routes de France, co-supervised with Cyrille Fauchard and Antoine Tonnoir on the resolution and simulation of the inverse problem in electromagnetic tomography, applications to civil engineering materials).

Image processing; From image segmentation under geometrical constraints (started with Carole Le Guyader and Dominique Apprato) to vision detection system based ML/DL tools (with Alexandre Leclerc, with Olivier Gibaru and Carlos Miranda from Buawei), we have developed many efficient methods in the last 25 years!

I insist on the Generalized Fast Marching methods (with Carole Le Guyader and Nicolas Forcadel) that is an excellent and efficient segmentation method. Recently, with Guzel Khayretdinova, we also have proposed a combined approximation and segmentation approach based on works from Dominique Apprato, Sylvie Vieira-Testé and Carole Le Guyader.

Shape optimization for 3D printing; This work is part of a long-standing collaboration with Dassault Systèmes, with a collaboration started in 2001 with David Bonner on many different 3D topics. The shape optimization is recent, coming from Martin Pierre Schmidt thesis. We wrote two (applied) papers with Laura Couret and Klaus Pedersen on this topic.

Keywords: Approximation, Signal and image processing, data modeling in medical sciences and geology, numerical analysis, optimization, segmentation, variational methods.

PhD supervisions

Current supervisions

Alexandre Leclerc (PhD, CIFRE Buawei, avec C. Le Guyader et C. Miranda).
Theau Cousin (postdoc, Scale Op project)

Past supervisions

Augustin Leclerc (PhD, with A. Tonnoir and H. Barucq, def. 2024)
Guzel Khayretdinova (co-tutelle Tomsk Russie with S. Kuksenko, def. nov 2025)
Théau Cousin (CIFRE Routes de France, with A. Tonnoir, C. Fauchard (Cerema), def. march 2024)
Imene Bouzarkouna (PhD with D. Baudry Cesi, def. 2021)
Martin Pierre. Schmidt (def. march 2020)
Aurélien Citrain (with H. Barucq, def. nov. 2019)
Soufia Benhida (cotutelle ENSA Agadir, avec A. Knippel def. dec. 2018)
Daniel Cervantes (UNAM Mexique, with P. Gonzalez Casanova, def. 2017)
Edson Miyaura (2012/16) avec LOFIMS
Theophile Chaumont-Frelet (with H. Barucq, def. nov 2015)
Solène Ozeré with C. Le Guyader (def. 2015)
Zacharie Alès (with A. Knippel, et LITIS)
Denis Brazey (TEB Prynel, with B. Portier)
Ratiba Derfoul (IFPEN, 2010-13, with C. Le Guyader 50%)
Marc Helbling (with D. Bonner, Cifre Dassault Sys. 2006-2010)
Aurélien Travert (with D. Bonner, Cifre Dassault Sys. 2002-2006)
Carole Le Guyader (2002-2004).

Research engineers/Postdoc : (recently) Guzel Khayretdinova (2025, PEPS AMIES CNRS), Océane Riga (2023, Intertwind), Zoé Lambert (Ingénieur de Recherche M2SiNum), Imene Khames (postdoc) projet M2NUM...