Data-driven sparse polynomial chaos expansion for models with dependent inputs

TL;DR

This paper introduces a data-driven method for constructing sparse polynomial chaos expansions that efficiently handle models with dependent inputs, improving stability and reducing data requirements.

Contribution

It proposes a recursive, correlation-based algorithm for building sparse PCEs for dependent inputs, addressing limitations of existing methods.

Findings

Reduces the number of observations needed for accurate PCEs

Enhances numerical stability and computational efficiency

Validated through four numerical examples

Abstract

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram-Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm.