Regularized infill criteria for multi-objective Bayesian optimization with application to aircraft design

Bayesian optimization is an advanced tool to perform ecient global optimization It consists on enriching iteratively surrogate Kriging models of the objective and the constraints both supposed to be computationally expensive of the targeted optimization problem Nowadays efficient extensions of Bayesian optimization to solve expensive multiobjective problems are of high interest The proposed method in this paper extends the super efficient global optimization with mixture of experts SEGOMOE to solve constrained multiobjective problems To cope with the illposedness of the multiobjective inll criteria different enrichment procedures using regularization techniques are proposed The merit of the proposed approaches are shown on known multiobjective benchmark problems with and without constraints The proposed methods are then used to solve a biobjective application related to conceptual aircraft design with ve unknown design variables and three nonlinear inequality constraints The preliminary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.

Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.

Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction

Ensuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433\% to 0.0163\%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82\% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3\%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.

Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf

High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft

Multidisciplinary design optimization (MDO) methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer, and categorical variables might arise during the optimization process, and practical applications involve a significant number of design variables. Recently, there has been a growing interest in mixed-categorical metamodels based on Gaussian Process (GP) for Bayesian optimization. In particular, to handle mixed-categorical variables, several existing approaches employ different strategies to build the GP. These strategies either use continuous kernels, such as the continuous relaxation or the Gower distance-based kernels, or direct estimation of the correlation matrix, such as the exponential homoscedastic hypersphere (EHH) or the Homoscedastic Hypersphere (HH) kernel. Although the EHH and HH kernels are shown to be very efficient and lead to accurate GPs, they are based on a large number of hyperparameters. In this paper, we address this issue by constructing mixed-categorical GPs with fewer hyperparameters using Partial Least Squares (PLS) regression. Our goal is to generalize Kriging with PLS, commonly used for continuous inputs, to handle mixed-categorical inputs. The proposed method is implemented in the open-source software SMT and has been efficiently applied to structural and multidisciplinary applications. Our method is used to effectively demonstrate the structural behavior of a cantilever beam and facilitates MDO of a green aircraft, resulting in a 439-kilogram reduction in the amount of fuel consumed during a single aircraft mission.

SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes

The Surrogate Modeling Toolbox (SMT) is an open-source Python package that offers a collection of surrogate modeling methods, sampling techniques, and a set of sample problems. This paper presents SMT 2.0, a major new release of SMT that introduces significant upgrades and new features to the toolbox. This release adds the capability to handle mixed-variable surrogate models and hierarchical variables. These types of variables are becoming increasingly important in several surrogate modeling applications. SMT 2.0 also improves SMT by extending sampling methods, adding new surrogate models, and computing variance and kernel derivatives for Kriging. This release also includes new functions to handle noisy and use multifidelity data. To the best of our knowledge, SMT 2.0 is the first open-source surrogate library to propose surrogate models for hierarchical and mixed inputs. This open-source software is distributed under the New BSD license.