M2 internship (H/F) - Model order reduction and data assimilation for smart monitoring of mechanical sy

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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