(Georgia Institute of Technology, 2023-06)
Mufti, Bilal; Perron, Christian; Gautier, Raphaël; Mavris, Dimitri N.
The parameterization of aerodynamic design shapes often results in high-dimensional design
spaces, creating challenges when constructing surrogate models for aerodynamic coefficients.
Active subspaces offer an effective way to reduce the dimensionality of such spaces, but
existing approaches often require a substantial number of gradient evaluations, making them
computationally expensive. We propose a multi-fidelity, model-based approach to finding
an active subspace that relies solely on direct function evaluations. By using both high- and
low-fidelity samples, we develop a model-based approximation of the projection matrix of the
active subspace. We evaluate the proposed method by assessing its active subspace recovery
characteristics and resulting model prediction accuracy for airfoil and wing drag prediction
problems. Our results show that the proposed method successfully recovers the active subspace
with an acceptable model prediction error. Furthermore, a cost vs. accuracy comparison with
the multi-fidelity gradient-based active subspace method demonstrates that our approach offers
comparable predictive performance with lower computational costs. Our findings provide
strong evidence supporting the usage of the proposed method to reduce the dimensionality of
design spaces when gradient samples are unavailable or expensive to obtain.
(Georgia Institute of Technology, 2022-06)
Mufti, Bilal; Chen, Mengzhen; Perron, Christian; Mavris, Dimitri N.
Modern design problems routinely involve high-dimensional inputs and the active subspace
has been recognized as a potential solution to this issue. However, the computational cost
for collecting training data with high-fidelity simulations can be prohibitively expensive. This
paper presents a multi-fidelity strategy where low-fidelity simulations are leveraged to extract
an approximation of the high-fidelity active subspace. Both gradient-based and gradient-free
active subspace methods are incorporated with the proposed multi-fidelity strategy and are
compared with the equivalent single-fidelity method. To demonstrate the effectiveness of our
proposed multi-fidelity strategy, the aerodynamic analysis of an airfoil and a wing are used
to define two application problems. The effectiveness of the current approach is evaluated
based on its prediction accuracy and training cost improvement. Results show that using a
low-fidelity analysis to approximate the active subspace of high-fidelity data is a viable solution
and can provide substantial computational savings, yet this is counterbalanced with slightly
worse prediction accuracy.