Investigation of Surrogate Modeling Options with High-Dimensional Input and Output

Abstract

Surrogate models are employed in engineering analysis to replace detailed physics-based models to achieve computational efficiency in problems that require multiple evaluations of the model. The accuracy of the surrogate model depends on the quality and quantity of data collected from the expensive model. This paper investigates surrogate modeling options for problems with high-dimensionality in both the input and output spaces. Several methods for reducing the output dimension are investigated, namely, singular value decomposition (SVD), random projection, randomized SVD, and diffusion map; similarly, several methods for input dimension reduction are investigated, namely, variance-based sensitivity analysis and active subspace discovery. The most effective combination of options for input and output dimension reduction is identified in a systematic way, followed by the construction of Gaussian process surrogate models in the low-dimensional space. The prediction error in the original space includes both the reconstruction error and surrogate error; a systematic approach is developed to quantify and compare the relative contributions of the two types of errors. The proposed general, systematic approach of exploring available options is applied to an aircraft fuselage panel. The effectiveness of various dimension reduction techniques with surrogate model construction are investigated in terms of accuracy and computational effort.