Optimization under uncertainties for multi-fidelity black-box simulators

Considering the sources of uncertainty in system design is essential in IFPEN applications for sustainable energy mix: e.g. to achieve the expected performance levels for an electric motor, for example, or for the reliability of a wind turbine. Indeed, these systems are subject to various sources of uncertainty: manufacturing dispersions, the characteristics of the materials (magnets or sheet metal for electric machines) or environmental conditions (wind and wave conditions for offshore wind turbines). The performance to be optimized or the constraints to be met are generally calculated using complex, time-consuming simulators, often considered as black boxes in the optimization process. The use of multi-fidelity simulations makes it possible to model the complex phenomena under study with varying levels of accuracy and computational cost, offering a compromise between computing performances and accuracy. Optimization under uncertainty applies to risk measures such as expectation (mean of performance), variance (dispersion of performance) or even an extreme quantile combining mean and variance. Calculating these risk measures for a given design requires a large number of simulations associated with Monte-Carlo sampling of the uncertain variables. The aim of this thesis is to propose an optimization approach based on approximations of the risk measures, which limits the computation time by using multi-fidelity simulations and adapted machine learning models. The extension of derivative-free optimization methods (Bayesian and deterministic approaches) to these variable-accuracy simulations will be studied, with the control of risk measure approximation errors: these errors can be mitigated by tuning the Monte-Carlo sample size and a careful choice of new simulations and the associated fidelity level along the optimization iterations

Keywords: Optimization, Multi-fidelity Simulators, Uncertainty Quantification, Surrogate Models

• Academic supervisor    Dr Céline HELBERT, UMR CNRS 5208, ORCID : 0000-0002-0085-5127
• Doctoral School    ED512 InfoMaths, Ecole Centrale de Lyon
• IFPEN supervisor    Dr Reda EL AMRI, mohamed-reda.el-amri@ifpen.fr, ORCID : 0000-0002-7641-9807 & Dr Delphine SINOQUET, ORCID : 0000-0002-3365-2051
• PhD location    Centrale Lyon and IFPEN Lyon, France
• Duration and start date    3 years, starting in the fourth quarter 2025 (Novembre 3)
• Employer    IFPEN
• Academic requirements    University Master’s Degree in Applied Mathematics and Statistics
• Language requirements    English level B2 (CEFR)
• Other requirements    Optimization, Statistics, Programming skills (Python/R)

To apply, please send your cover letter and CV to the IFPEN supervisor indicated here below.