Divide and Conquer: An Incremental Sparsity Promoting Compressive Sampling Approach for Polynomial Chaos Expansions

TL;DR

This paper presents an incremental sparsity-promoting algorithm for Polynomial Chaos expansions that improves recovery accuracy and reduces model dimensionality by exploring sub-dimensional expansions and removing uninfluential parameters.

Contribution

The proposed incremental algorithm enhances sparse recovery of Polynomial Chaos expansions by promoting sparsity and reducing dimensionality more effectively than conventional methods.

Findings

Outperforms traditional compressive sampling in sparsity and accuracy

Reduces dimensionality of Polynomial Chaos models

Demonstrated success across four numerical examples

Abstract

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional expansions for a sparser recovery, and shows success when removal of uninfluential parameters that results in a lower coherence for measurement matrix, allows for a higher order and/or sparser expansion to be recovered. The incremental algorithm effectively searches for the sparsest PC approximation, and not only can it decrease the prediction error, it can also reduce the dimensionality of PCE model. Four numerical examples are provided to demonstrate the validity of the proposed approach. The results from these examples show that the incremental algorithm substantially outperforms conventional compressive sampling approaches for PCE, in terms of both solution sparsity and prediction error.