(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.