Kade Carlson | Searcharxiv

arXiv2025

Multiobjective Aerodynamic Design Optimization of the NASA Common Research Model

Aircraft aerodynamic design optimization must account for the varying operating conditions along the cruise segment as opposed to designing at one fixed operating condition, to arrive at more realistic designs. Conventional approaches address this by performing a ``multi-point'' optimization that assumes a weighted average of the objectives at a set of sub-segments along the cruise segment. We argue that since such multi-point approaches are, inevitably, biased by the specification of the weights, they can lead to sub-optimal designs. Instead, we propose to optimize the aircraft design at multiple sub-segments simultaneously -- that is, via multiobjective optimization that leads to a set of Pareto optimal solutions. However, existing work in multiobjective optimization suffers from (i) lack of sample efficiency (that is, keeping the number of function evaluations to convergence minimal), (ii) scalability {in the absence of derivative information}, and (iii) the ability to generate a batch of iterates for synchronous parallel evaluations. To overcome these limitations, we {apply} a novel multiobjective Bayesian optimization methodology {for aerodynamic design optimization} that demonstrates improved sample efficiency and accuracy compared to the state of the art. Inspired by Thompson sampling, our approach leverages Gaussian process surrogates and Bayesian decision theory to generate a sequence of iterates according to the probability that they are Pareto optimal. Our approach, named batch Pareto optimal Thompson sampling (\qpots)\footnote{Here, $q$ stands for selecting a batch of $q$ iterates at every step.}, demonstrates superior empirical performance on a variety of synthetic experiments as well as a $24$ dimensional two-objective aerodynamic design optimization of the NASA common research model. We also provide open-source software of our methodology {and experiments}.

math.OC↗

arXiv2024

Multifidelity Cross-validation

Emulating the mapping between quantities of interest and their control parameters using surrogate models finds widespread application in engineering design, including in numerical optimization and uncertainty quantification. Gaussian process models can serve as a probabilistic surrogate model of unknown functions, thereby making them highly suitable for engineering design and decision-making in the presence of uncertainty. In this work, we are interested in emulating quantities of interest observed from models of a system at multiple fidelities, which trade accuracy for computational efficiency. Using multifidelity Gaussian process models, to efficiently fuse models at multiple fidelities, we propose a novel method to actively learn the surrogate model via leave-one-out cross-validation (LOO-CV). Our proposed multifidelity cross-validation (\texttt{MFCV}) approach develops an adaptive approach to reduce the LOO-CV error at the target (highest) fidelity, by learning the correlations between the LOO-CV at all fidelities. \texttt{MFCV} develops a two-step lookahead policy to select optimal input-fidelity pairs, both in sequence and in batches, both for continuous and discrete fidelity spaces. We demonstrate the utility of our method on several synthetic test problems as well as on the thermal stress analysis of a gas turbine blade.

stat.CO↗