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International audience; This work aims at proposing an aerodynamic design optimization methodology entirely based on Computer-Aided Design (CAD) representations, yielding a fully integrated geometry-simulation-optimization framework. Specifically, the geometry to optimize is defined thanks to CAD standards, like Non-Uniform Rational B-Splines (NURBS); the resolution of compressible Euler / Navier-Stokes equation is achieved using a Discontinuous Galerkin (DG) method based on rational Bézier elements with adaptive mesh refinement, which is geometrically exact with respect to CAD boundaries; The global optimization of CAD control points is carried out using a Bayesian Optimization method. The whole design chain is therefore consistent with respect to the CAD geometry. The proposed approach is demonstrated for the optimization of an airfoil in transonic regime.

International audience; We propose a Bayesian approach for parameter uncertainty quantification in macroscopic traffic flow models from cross-sectional data. A bias term is introduced and modeled as a Gaussian process to account for the traffic flow models limitations. We validate the results comparing the error metrics of both first and second order models, showing that second order models globally perform better in reconstructing traffic quantities of interest.

International audience; A major difficulty in aerodynamic design is related to the multiplicity of geometrical representations handled during the optimization process. From high-order Computer-Aided Design (CAD) objects to discrete mesh-based descriptions, several geometrical transformations have to be performed, that considerably impact the accuracy, the robustness and the complexity of the design loop. This is even more critical when Multiphysics applications are targeted, including moving bodies.To overcome this limitation, we present here a fully integrated methodology that combines ideas from Iso-Geometric Analysis (IGA) and high-order Discontinuous Galerkin methods, within an Arbitrary Lagrangian-Eulerian (ALE) formulation for compressible Navier-Stokes equations. The resulting approach relies on a single geometrical representation, based on Non-Uniform Rational B- Splines (NURBS), that allows to achieve geometrically exact simulations with adaptive local refinements and moving interfaces.We consider as demonstration the optimization of a morphing airfoil. The profile is defined by two cubic NURBS curves, whose deformations are controlled in terms of frequency, amplitude and length, while a C1 regularity is maintained during the whole process. A multi-objective Bayesian optimization is carried out to select the most promising control parameters with respect to the time-averaged lift, the instantaneous minimum lift and the time-averaged actuation power.

One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by building a surrogate model of the black-box to simultaneously select multiple designs via an infill criterion. Still, despite the increased availability of computing resources that enable large-scale parallelism, the strategies that work for selecting a few tens of parallel designs for evaluations become limiting due to the complexity of selecting more designs. It is even more crucial when the black-box is noisy, necessitating more evaluations as well as repeating experiments. Here we propose a scalable strategy that can keep up with massive batching natively, focused on the exploration/exploitation trade-off and a portfolio allocation. We compare the approach with related methods on noisy functions, for mono and multi-objective optimization tasks. These experiments show orders of magnitude speed improvements over existing methods with similar or better performance.

This chapter addresses the question of how to efficiently solve many-objective optimization problems in a computationally demanding black-box simulation context. We shall motivate the question by applications in machine learning and engineering, and discuss specific harsh challenges in using classical Pareto approaches when the number of objectives is four or more. Then, we review solutions combining approaches from Bayesian optimization, e.g., with Gaussian processes, and concepts from game theory like Nash equilibria, Kalai-Smorodinsky solutions and detail extensions like Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding algorithms and provide some illustrating results.

International audience; In this work we present a fully integrated framework for aerodynamic shape optimisation. In order to develop an efficient design chain, a high level of automation is required. To this end, we propose an isogeometric approach, in which the same mathematical representation is adopted for the shape to optimize, the computational domain and the physical solution, without any geometrical approximation. It results in a tight coupling between the Computer Aided Design (CAD) tool, the mesh generation / adaption and the Computational Fluid Dynamics (CFD) solver. As a consequence, all transfers of information between the components of the design loop are significantly facilitated. The compressible Navier-Stokes equations are solved using the Isogeometric Discontinuous Galerkin scheme. The flow solver is then coupled with an Efficient Global Optimisation (EGO) algorithm to complete the design chain. We first demonstrate the capability of the developed methodology by considering a classic drag reduction problem, in which an airfoil shape is optimised for a transonic flow condition. Since the position of the shock on the airfoil surface is a function of the geometry, traditional approaches require highly refined meshes in a large area to properly capture the discontinuity for all the possible designs. However, thanks to the isogeometric formulation, we can exploit an Adaptive Mesh Refinement technique presented to further reduce the computational costs by refining locally the mesh while preserving exactly the geometry. As a second test case, we study an active morphing technique to control the boundary layer separation over an airfoil. The Arbitrary Lagrangian-Eulerian approach proposed is used for solving the flow equations on the time-dependent deforming domain. The isogeometric methodology allows an accurate description and a control of the regularity of the deformation of the airfoil surface. The EGO algorithm is thus used to find the optimal set of parameters for the morphing technique.