homepage of Claire Schnoebelen

Research

Progressive Gradient Descent in Sparse Identification of Non-Linear Dynamics for Hamiltonian Learning (work in progress).
In this project, we study the possibilities of using Sparse Identification of Non-linear Dynamics (SINDy) method to learn Hamiltonian functions of PDEs. We Conducting tests on waves and Korteweg-de Vries equations, we highlighted some aspects of the optimisation process that we must take into account to perform it efficiently.
Symplectic Neural Operators for PDEs (work in progress)
We are considering symplectic neural operators that mimics SympNet an that we would like to apply to PDEs. We are exploring both spectral and spatial layers.
Quantitative h-principle for isosymplectic embeddings and consequences on symplectic model reduction (work in progress)
In this project, we want to show quantitative $h$-principle for isosymplectic embeddings using tools introduced in Quantitative h-principle in symplectic geometry (L. Buhovsky and E. Opshtein, 2016). We also explore the consequences on Hamiltonian model order reduction by asking what conditions must satisfy the decoder to be in position to hope finding an accurate Hamiltonian in the reduced space.

Trajectories generated by a parametrised Hamiltonian of a SINDy-type model at the beginning of the training (color, left) and at the end (color, right) and ground truth (seven Korteweg-de Vries trajectories, dashed gray). Detailed about the training method and results can be found here.

Past projects

During my master studies, I had the opportunity to work on several projects about discrete differential geometry, reduced modelling and structure preserving methods, under the supervision of Emmanuel Franck, Laurent Navoret and Emmanuel Opshtein. I studied for instance dimensionality reduction methods such as Isomap, Eigenmap and Proper Symplectic Decomposition with quadratic corrections, hyperreduction throught reproducing kernel spaces and integration within mimetic framework.

2023: Non-linear reduced models for Hamiltonian systems (master dissertation, pdf)
2023: Structure preserving methods on staggered grids (master project, pdf)
2022: Discrete differential geometry and dimensionality reduction (master internship, pdf)
2022: Reduced order models for partial differential equations (master project, pdf)

Teaching

Spring 2025: Géométrie axiomatique at Université de Strasbourg
Construction of Euclidean geometry from Hilbert axioms for first year bachelor students (lessons in small classes and exercise sessions).
Fall 2025: Informatique S3 at Université de Strasbourg
Programmation in Python for second year bachelor students (exercise sessions).
Fall 2025: Techniques d'analyse numérique at Université de Strasbourg
Numerical analysis for third year bachelor students (exercise sessions).
Fall 2024: Informatique S5 at Université de Strasbourg
Introduction to programmation in C++ and algorithmic for third year bachelor students (exercise sessions).
Spring 2024 and spring 2025: Mathématiques pour la biologie at Université de Strasbourg
Calculus for first year bachelor students in biology (exercise sessions).
Fall 2023: Mathématiques pour les sciences at Université de Strasbourg
Calculus and analysis for first year bachelor students in physical sciences (lessons in small classes and exercise sessions).

Conferences and seminars

July 2026: Eccomas Conference, München
to be coming (talk in minismyposium "MS187 Structure-Preserving Scientific Machine Learning and Neural Networks")
June 2026: SciCADE Conference, Edimbourg
to be coming (contributed talk)
June 2026: Workshop on Machine Learning and Automatic Differentiation in JAX for Scientific Computing, Strasbourg
to be coming (talk and practical session)
September 2025: Enumath Conference, Heidelberg
Learning Hamiltonian functions of PDEs via SINDy method. (talk)
July 2025: Matheors Days, Saint-Marie-aux-Mines
A very brief introduction to h-principle. (talk)
June 2025: SMAI Congress, Carcans
Learning Hamiltonian functions. (talk)
March 2025: EMS SciML meeting, Milano
Learning Hamiltonian functions. (poster)
January 2025: IRMA PhD seminar, Strasbourg
Introduction to Nambu structures. (talk)
July 2024: SciML workshop, Strasbourg
Learning Hamiltonian functions of ODEs and PDEs. (poster)
June 2024: Summer school on h-principle, Madrid
February 2024: IRMA PhD seminar, Strasbourg
Two examples of non-linear data reduction methods: Isomap and Eigenmap. (talk)
November 2023: NumKin workshop, Garching.
September 2023: Summer school Geometry and Data, Strasbourg.
September 2022: Summer school Deep Learning and Applications, Strasbourg.
January 2022: Master class EDP, Optimisation et Données, Strasbourg.

Outreach

March 2024: Outreach presentation for secondary school students at Lycée Jean-Jacques Henner, Altkirch
Aperçus de thèses en mathématiques. ("A glimpse of PhD in mathematics") (talk)
In April 2025, I took part in the organisation of the Rendez-vous des jeunes mathématiciennes et Informaticiennes at Université de Strasbourg. I was responsible for legal matters related to GDPR and reception of minors and was in contact with the competent services of the Bas-Rhin department.
In April 2024, I took part in the organisation and supervision of the Rendez-vous des jeunes mathématiciennes et Informaticiennes at Université de Strasbourg. I co-supervised a research group and some activities during the three days.

Miscellaneous

Between December 2023 and December 2025, I served as IRMA's representative on the management committee of IRMIA++ Young Researcher Budget.
During this period, I helped organise external speakers in IRMA PhD seminar and I co-organised the IRMIA++ Young Researcher Cohesion Day in April 2024 with Yassin Khalil and Thibaut Eloy.
In October 2024, I won a first prize at the poster session of École Doctorale MSII of Université de Strasbourg.
In May 2024, I participated to an AMIES Semaine d'Étude Maths-Entreprises at Université Savoie Mont-Blanc.
I was a member of the team working on the subject Optimisation du système hydraulique des Wateringues ("Optimisation of the Wateringues's hydraulic system") under the supervision of Antoine Vollant from SETEC-Hydratec.

Education

In 2023, I obtained the master diploma in applied mathematics Calcul Scientifique et Mathématiques de l'Information ("Scientific Computation and Mathematics of Information") with mention Magistère de mathématique at UFR de Mathématiques et d'Informatique of Université de Strasbourg.
I followed lessons on machine learning, data analysis, numerical analysis, data bases, programmation in C++, Python and Rust, graphs, functionnal analysis, parallel computation, PDEs, optimal control and optimisation.
Between 2021 and 2023, I followed a training programm about interdisciplinarity entitled DU Mathématiques et Applications, Recherche et Interactions. In this context, I was part of the group of students who worked on a project entitled Plongements hyperboliques de graphes hiérarchiques ("Hyperbolic embeddings of hierarchic graphs") under the supervision of Emmanuel Opshtein.
In 2021, I obtained a bachelor in mathematics at Université de Strasbourg. My dissertation was about Cartan-Hadamard theorem in the case of surfaces in dimension three.
In 2020, I obtained a bachelor in geography at Université de Strasbourg.