Data-driven dimensionally decomposed generalized polynomial chaos expansion for forward uncertainty quantification

2025/10/26 by Choi, Hojun, Heo, Eunho, Lee, Dongjin
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2510.22642

Abstract

Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However, constructing the measure-consistent orthonormal polynomial bases in DD-GPCE requires prior knowledge of input distributions, which is often unavailable in practice. This work introduces a data-driven DD-GPCE method that eliminates the need for such prior knowledge, extending its applicability to UQ with high-dimensional inputs. Input distributions are inferred directly from sample data using smoothed-bootstrap kernel density estimation (KDE), while the DD-GPCE framework enables KDE to handle high-dimensional inputs through low-dimensional marginal estimation. We then use the estimated input distributions to perform a whitening transformation via Monte Carlo Simulation, which enables generation of measure-consistent orthonormal basis functions. We demonstrate the accuracy of the proposed method in both mathematical examples and stochastic dynamic analysis for a practical three-dimensional mobility design involving twenty random inputs. The results indicate that the proposed method produces more accurate estimates of the output mean and variance compared to the conventional data-driven approach that assumes Gaussian input distributions.

Citations

• Extension of graph-accelerated non-intrusive polynomial chaos to high-dimensional uncertainty quantification through the active subspace method
• Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging
• Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion
• Nonparametric Uncertainty Quantification for Single Deterministic Neural Network
• A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions
• SciPy 1.0: fundamental algorithms for scientific computing in Python
• Mathematical Properties of Polynomial Dimensional Decomposition

Related

• Deep Adaptive Arbitrary Polynomial Chaos Expansion: A Mini-data-driven Semi-supervised Method for Uncertainty Quantification
• SeAr PC: Sensitivity Enhanced Arbitrary Polynomial Chaos
• Uncertainty Quantification for Machine Learning-Based Prediction: A Polynomial Chaos Expansion Approach for Joint Model and Input Uncertainty Propagation
• Deep Polynomial Chaos Expansion
• An Empirical Chaos Expansion Method for Uncertainty Quantification