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M2 internship (H/F) - Model order reduction and data assimilation for smart monitoring of mechanical systems Job Opening In Paris – Now Hiring CNRS

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

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Job description

Informations générales

Intitulé de l'offre : M2 internship (H/F) - Model order reduction and data assimilation for smart monitoring of mechanical systems

Référence : UMR8006-DIMGOU-001

Lieu de travail : PARIS 13

Pays : France

Date de publication : vendredi 10 octobre 2025

Type de contrat : Convention de stage

Durée du contrat : 6 mois

Date d'embauche prévue : 2 février 2026
Quotité de travail : Complet

Niveau de diplôme préparé : BAC+5

BAP : C - Sciences de l'Ingénieur et instrumentation scientifique


Description du poste


Context
Smart monitoring of mechanical systems (., 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 (., damped vibrations, wave propagation, thermal diffusion).

This harmonized library will serve as a reference framework for this upcoming project to:
•Compare different ROM approaches (., POD-Galerkin, LSPG [2], structure-preserving, auto-encoder) and DA techniques (., 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-informed machine learning for structural health monitoring.

Structural health monitoring based on data science techniques (pp.

347-367).
[5] Goutaudier, D., Gendre, D., Kehr-Candille, V., & Ohayon, R.

(2020).

Single-sensor approach for impact localization and force reconstruction by using discriminating vibration modes.

Mechanical Systems and Signal Processing, 138, 106534.


Descriptif du profil recherché


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.



Informations complémentaires


Possibility of PhD continuation: yes, if successful internship (ANR funding secured)

Required Skill Profession

Physical Scientists


  • Job Details

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