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Daniel Guggenheim School of Aerospace Engineering

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A Multi-Fidelity Approximation of the Active Subspace Method for Surrogate Models with High-Dimensional Inputs

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.

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