Context and Motivation
Engineering design optimization faces significant challenges when dealing with computationally
expensive simulations (ranging from 10 minutes to several days per evaluation) and inherent
uncertainties in operating conditions and manufacturing tolerances. Traditional deterministic
optimization approaches often yield designs that are sensitive to these uncertainties, leading to
performance degradation or constraint violations in real-world conditions.
The need to balance multiple objectives while satisfying probabilistic constraints, such as reliability requirements, is paramount in industries like aerospace, automotive, and energy. This internship focuses on enhancing state-of-the-art robust optimization methodologies to address multiobjective problems under uncertainties, with a particular emphasis on handling low-probability events and accelerating the optimization process using advanced deep learning techniques.Objectives
The SAMATA framework [1] provides a promising Bounding Box Stochastic approach for multiobjective optimization under uncertainty using Gaussian Processes. However, its current formulation faces limitations in handling extreme quantiles and low-probability failure events, which are critical for reliability-based design optimization.
This internship aims to extend the SAMATA methodology [1] by integrating advanced infill
sampling strategies adapted from eAKMCS [2], suitable for low failure probability and extreme
quantiles. To further accelerate the aerodynamic optimization process, data-driven deep learning techniques, such as DeepONet [4], will be explored to obtained improved surrogates for faster shape optimization.The work breakdown of the internship is as follows:
- Extend the SAMATA framework [1] for extreme quantile estimation using eAKMCS
[2].- Validate the methodology on analytical test problems.
- Apply the methodology to a realistic aerodynamic shape optimization test case, specifically
2D flow around airfoils under uncertain operational conditions (e.g., Mach number,
angle of attack), using CST parametrization.- Investigate deep learning acceleration using field-based neural networks [4], leveraging
the AirFRANS dataset [3].By the end of the internship, you will have gained hands-on experience in implementing stateof-
the-art robust optimization methodologies and recent neural network architectures, applying
them to a realistic numerical optimization test case. You will also have a deeper understanding
of how to leverage these powerful mathematical tools to address complex optimization problems relevant to industry.Requirements and Appreciated Skills
- Strong programming skills
- Interest in CFD and machine learning
- Experience with CFD tools (e.g., SU2, OpenFOAM) and Python (PyTorch, JAX)
Contact:
heloise.beaugendre@math.u-bordeaux.fr, pietro.congedo@inria.fr, nassim.razaaly@ensma.fr
