High-Dimensional Uncertainty Quantification Using Stochastic Galerkin and Tensor Decomposition

Abstract

This article investigates the application of tensor decomposition and the stochastic Galerkin method for the uncertainty quantification of complex systems characterized by high parameter dimensionality. By employing these methods, we construct surrogate models aimed at efficiently predicting system output uncertainty. The effectiveness of our approaches is demonstrated through a comparative analysis of accuracy and central processing unit (CPU) cost with conventional Galerkin methods, using two transmission line circuit examples with up to 25 parameters.