Data-driven sparse polynomial chaos expansion for models with dependent inputs
This work addresses a domain-specific problem for engineering applications involving uncertainty quantification with dependent inputs, representing an incremental improvement over existing methods.
The paper tackles the problem of building polynomial chaos expansions (PCEs) for models with dependent inputs, which is challenging due to limitations in computational efficiency and distribution assumptions of existing methods. The proposed data-driven algorithm reduces the number of required observations and improves numerical stability and computational efficiency, as validated through four numerical examples.
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.