Gradient-informed basis adaptation for Legendre Chaos expansions

TL;DR

This paper introduces a gradient-informed basis adaptation method for Polynomial Chaos expansions that leverages active subspace discovery to reduce dimensionality, leading to computational savings and accurate statistical estimations.

Contribution

It proposes a novel approach combining basis adaptation with active subspace discovery for efficient polynomial chaos expansions in high-dimensional settings.

Findings

Significant computational savings demonstrated.

High accuracy in estimating statistics achieved.

Applicable to generalized Polynomial Chaos with 1D active subspaces.

Abstract

The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits most of its variability. In the case where a 1-dimensional active subspace exists, the methodology can be applicable to generalized Polynomial Chaos expansions, thus enabling the projection of a high dimensional input to a single input variable and the efficient estimation of a univariate chaos expansion. Attractive features of this approach, such as the significant computational savings and the high accuracy in computing statistics of interest are investigated.