An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification

Abstract

The computational costs of surrogate model-assisted uncertainty quantification methods become intractable for high dimensional problems. However, many high-dimensional problems are intrinsically low dimensional, if the output response exhibits some special structure that can be exploited within a low-dimensional subspace, known as the active subspace in the literature. Active subspace extracts linear combinations of all the original inputs, which may obscure the fact that only several inputs are active in the low-dimensional space. Motivated by this fact, this paper proposes a new surrogate modeling method which imposes sparsity in the active subspace to achieve a better performance for dimension reduction. Information given by sparse active subspace is integrated in the kernel structure of the support vector regression model to ensure superior performance for high dimensional problems. We demonstrate the proposed method on several benchmark applications, comprising an analytical function and two engineering applications of increasing dimensionality and complexity.