Postdoc - Bayesian calibration with model error in structural dynamics

INRIA; France; On-site; EUR 27,000 - 33,000; Full time

Job summary

INRIA Saclay - Île-de-France invites applications for a postdoctoral position in Bayesian calibration of numerical models for structural dynamics. The project focuses on calibrating uncertain parameters to align FE/numerical responses with measured data, using Bayesian inference and model updating techniques.

The candidate will work within the Platon team at CMAP, collaborating with experts in uncertainty quantification and engineering applications.

Qualifications

• PhD required in mechanical engineering or applied mathematics or related field.
• Proficient scientific computing and exposure to numerical modeling.
• Experience with uncertainty quantification and structural dynamics is highly desirable.

Responsibilities

• Develop a Bayesian calibration framework for structural dynamics problems.
• Identify key quantities for calibration (e.g., resonant frequencies, damping).
• Compare proposed methods against state-of-the-art approaches.
• Implement, test, and validate surrogate-based strategies and code.

Skills

Scientific computing

Uncertainty quantification

Structural dynamics

Education

PhD in mechanical engineering

Tools

Python

MATLAB

Job description

Organisation/Company INRIA Department Centre de Recherche INRIA Saclay - Île-de-France Research Field Engineering » Mechanical engineering Mathematics » Applied mathematics Researcher Profile Recognised Researcher (R2) Positions Postdoc Positions Application Deadline 16 Oct 2026 - 12:00 (Europe/Paris) Country France Type of Contract Temporary Job Status Full-time Offer Starting Date 1 Jan 2027 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

• Salary: gross monthly salary of about 2700€
• Funding: ANR JCJC MeMora

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.

Supervision

The postdoc will be supervised by E. Denimal Goy expert in structural dynamics and uncertainty quantification; and by P.M. Congedo 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.

[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).

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.