Le Centre national de la recherche scientifique est un organisme public de recherche pluridisciplinaire placé sous la tutelle du ministère de l’Enseignement supérieure et de la Recherche. Créé en 1939 et dirigé par des scientifiques, il a pour mission de faire progresser la connaissance et être utile à la société dans le respect des règles d’éthique, de déontologie et d’intégrité scientifique.

Poste :
Context
Smart monitoring of mechanical systems (e.g., engineering structures, industrial processes) requires accurate numerical models that can be exploited in real time [1]. Reduced Order Modeling (ROM) and Data Assimilation (DA) are key tools for designing efficient monitoring solutions. In preparation for an upcoming ANR-funded project starting in 2026, we aim to develop a library of models covering various physical phenomena (e.g., damped vibrations, wave propagation, thermal diffusion). This harmonized library will serve as a reference framework for this upcoming project to:
• Compare different ROM approaches (e.g., POD-Galerkin, LSPG [2], structure-preserving, auto-encoder) and DA techniques (e.g., EKF, 4D-Var, PBDW [3]) for smart monitoring applications;
• Explore physics-informed Artificial Intelligence (AI) approaches adapted to practical constraints of smart monitoring [4].

Internship objectives
The intern will be responsible for:
1. Developing a collection of numerical test cases representative of key physical behaviors relevant to smart monitoring.
2. Implementing ROM methodologies in a harmonized and reusable framework.
3. Evaluating a data assimilation technique under development at the laboratory.
4. Delivering a documented GitHub library including reproducible scripts.

Opportunity for PhD continuation
This internship is linked to a funded ANR JCJC project, SPARSE-SHM (Sparse structural health monitoring using signature-informed hybrid modeling). The goal will be to develop an innovative Structural Health Monitoring (SHM) framework capable of operating with a very limited number of sensors. The core concept relies on signature-informed modeling. The principle is to extract only essential and robust information about key parameters of interest from measurements. A proof of concept has been demonstrated for an SHM application [5].
The PhD will involve theoretical developments (formulation of signature-informed ROMs), advanced numerical methods (coupling ROM–data assimilation–AI), and experimental validation (SHM demonstrators).

References
[1] Chinesta, F., Cueto, E., Abisset-Chavanne, E., Duval, J. L., & Khaldi, F. E. (2018). Virtual, digital and hybrid twins: a new paradigm in data-based engineering and engineered data. (No. ART-2018-109564).
[2] Carlberg, K., Farhat, C., Cortial, J., & Amsallem, D. (2013). The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. Journal of Computational Physics, 242, 623-647.
[3] Maday, Y., Patera, A. T., Penn, J. D., & Yano, M. (2015). A parameterized‐background data‐weak approach to variational data assimilation: formulation, analysis, and application to acoustics. International Journal for Numerical Methods in Engineering, 102(5), 933-965.
[4] Cross, E. J., Gibson, S. J., Jones, M. R., Pitchforth, D. J., Zhang, S., & Rogers, T. J. (2021). Physics-inf
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Le Centre national de la recherche scientifique est l’une des plus importantes institutions publiques au monde : 34 000 femmes et hommes (plus de 1 000 laboratoires et 200 métiers), en partenariat avec les universités et les grandes écoles, y font progresser les connaissances en explorant le vivant, la matière, l’Univers et le fonctionnement des sociétés humaines. Depuis plus de 80 ans, y sont développées des recherches pluri et interdisciplinaires sur tout le territoire national, en Europe et à l’international. Le lien étroit que le CNRS tisse entre ses missions de recherche et le transfert vers la société fait de lui un acteur clé de l’innovation en France et dans le monde. Le partenariat qui le lie avec les entreprises est le socle de sa politique de valorisation et les start-ups issues de ses laboratoires (près de 100 chaque année) témoignent du potentiel économique de ses travaux de recherche.

Profil echerché :
Profile
• Final-year engineering student or Master 2 student in computational mechanics, applied mathematics, or scientific computing.
• Interest in discovering research and potentially pursuing a PhD.

Expected skills
• Solid background in numerical methods (PDEs, finite elements, scientific computing).
• Interest in modeling, model order reduction, and data assimilation.
• Proficiency in one scientific programming language: MATLAB, Python, or Julia.


Conditions Particulières :