Post-Doctoral Research Visit F/M Bayesian calibration with model error in structural dynamics

1000scholars; Palaiseau; On-site; EUR 27,000 - 33,000; Full time

Job summary

Inria Saclay, in collaboration with the PLATON Inria project-team, seeks a postdoctoral researcher to develop Bayesian calibration frameworks for structural dynamics. The role focuses on calibrating FE models using observed data, accounting for model error, and comparing to state-of-the-art methods.

The candidate will implement surrogate-based strategies and contribute to publications. The position is based at Inria Saclay, with a gross monthly salary of about 2700€ for 12 months, starting by

Qualifications

• PhD in mechanical engineering or applied mathematics is required.
• Experience with Bayesian calibration and uncertainty quantification is essential.
• Strong scientific computing and programming skills are expected.

Responsibilities

• Develop a Bayesian calibration framework for structural dynamics.
• Identify relevant calibration quantities (e.g., resonant frequencies, damping).
• Implement and test calibration algorithms on mechanical models.
• Validate algorithms on different test cases and document results.
• Prepare journal articles and reports.

Skills

Bayesian methods

Uncertainty quantification

Scientific computing

Model calibration

Education

PhD in mechanical engineering or applied mathematics

Job description

Context

Supervised by:
E. Denimal Goy at Inria Saclay, PLATON Inria project-team; Center for Applied Mathematics (Ecole Polytechnique); expert in structural dynamics and uncertainty quantification, Pietro M. Congedo at Inria Saclay, PLATON Inria project-team; Center for Applied Mathematics (Ecole Polytechnique); expert uncertainty quantification methods for engineering applications.

The work will be conducted in the Platon team, a joint research group between Ecole Polytechnique and CNRS, hosted by the Center for Applied Mathematics (CMAP) of École Polytechnique. The Platon project-team focuses on developing innovative methods and algorithms for uncertainty management in numerical models, including advanced calibration strategies from data (observations, measurements, other model predictions) and uncertainty reduction.

General details

Duration: 12 months

Starting date: no later than January 2027

Location: Inria Saclay, 1 rue Honoré d'Estienne d'Orves, 91120 Palaiseau, FRANCE

Salary: gross monthly salary of about 2700€

Funding: ANR JCJC MeMoRa

Assignment

Project description and objectives

Predicting the dynamic behavior of mechanical and civil engineering structures is a central concern throughout their design and operational life, whether to ensure structural integrity under vibration and dynamic loading, or to anticipate fatigue and durability issues. Numerical models, and finite element (FE) models in particular, have become the primary tool for addressing these challenges, offering a flexible and cost-effective means of simulating structural response before physical testing.

Yet for these models to make accurate predictions, their parameters must reflect the real structure and the real environment, not just the nominal values assumed during design. Model calibration, also referred to as model updating, meets this need by adjusting uncertain or poorly known model parameters so that the numerical response matches measured data. In structural vibration, this is typically done using modal parameters (natural frequencies, mode shapes, damping ratios) or frequency response functions obtained from experimental campaigns.

This process is essential to improve the predictive capability of the model. Bayesian approaches are classical techniques to perform this calibration process. They rely on the assumption that the discrepancy between the numerical solver and the experimental data are explained by the experimental noise.

However, the models are built upon simplifying assumptions such as geometry, material properties, boundary conditions, joint behavior, etc. This leads inevitably to discrepancies between numerical predictions and experimental observations, which must be accounted for during the calibration process. In this context, Bayesian approaches can be used to explicitely account for uncertainties arising from measurement noise, model-form error, and parameter variability. The results obtained with such approaches provide more robust and physically meaningful estimates of the calibrated parameters along with quantified confidence in the model predictions. Recent works in the team have focused on the development of such frameworks for academic test cases [1,2].

Additionally, the quality of the calibration depends on the choice of the quantities used to perform it [3]. If these quantities are not sufficiently sensitive to the parameters being calibrated, the identification process becomes ill-posed, leading to poorly constrained or unreliable parameter estimates.

The objective of the postdoc is to develop a Bayesian calibration framework to account for model error in the context of structural dynamics. The following objectives have been identified:

• develop a Bayesian model calibration with model error framework for structural dynamics,
• identify relevant quantities for the calibration (resonance frequencies, vibration amplitude, etc),
• compare the results to state-of-the-art methods,
• accelerate this framework, using surrogate based strategies for example.

The person recruited will have to numerically implement, test and compare the different identified approaches developed during the postdoc.

Biblio

[1] Kahol, O., Congedo, P.M., Le Maitre, O. and Goy, E.D., 2025. {Efficient treatment of the model error in the calibration of computer codes: the Complete Maximum a Posteriori method.} International Journal for Uncertainty Quantification, 15(5).

[2] Kahol, O., Le Maître, O., Marco Congedo, P. and Denimal Goy, E., 2026. {Surrogate-based strategies for accelerated Bayesian calibration of computer codes with Complete Maximum a Posteriori estimation of model error.} Journal of Mechanical Design, 148(9), p.091706.

[3] Delette, N., Goy, E.D., Pfister, J.L., El Amri, R. and Mevel, L., 2025, May. {Model updating of rotating wind turbines using operational modal analysis and Floquet mode decomposition}. In IOMAC 2025-11th International Operational Modal Analysis Conference (pp. 1-7).

Main activities

• Literature review
• Development of calibration algorithms with model error
• Implementation and simulation of mechanical models
• Implementation of associated algorithms and validation on different test cases
• Writting documentation, reports and journal articles
• Prsentation (work progress meetings, team meetings, ANR consortiums meetings, conferences)

Skills

Candidates must hold a PhD in mechanical engineering, applied mathematics or a related discipline with background in at least one of these fields: structural dynamics, model calibration, uncertainty quantification or related fields. In particular, candidates must be proficient scientific computing.

Applicants should submit a detailed academic CV with history of scientific production, evaluation documents of their PhD if available and a cover letter detailing the knowledge, skills and experience you think make you the right candidate for the job.

For further details, please contact E. Denimal Goy (enora.denimal-goy [at] inria.fr).