A Statistical Parsimony Method for Uncertainty Quantification of FDTD Computation Based on the PCA and Ridge Regression

The nonintrusive polynomial chaos (NIPC) expansion method is one of the most frequently used methods for uncertainty quantification (UQ) due to its high computational efficiency and accuracy. However, the number of polynomial bases is known to substantially grow, as the number of random parameters increases, leading to excessive computational cost. Various sparse schemes such as the least angle regression method have been utilized to alleviate such a problem. Nevertheless, the computational cost associated with the NIPC method is still nonnegligible in systems that consist of a high number of random parameters. This paper proposes the first versatile UQ method, which requires the least computational cost while maintaining the UQ accuracy. We combine the hyperbolic scheme with the principal component analysis method and reduce the number of polynomial bases with the simpler procedure than currently available, keeping most information in the system. The ridge regression method is utilized to build a statistical parsimonious model to decrease the number of input samples, and the leave-one-out cross-validation method is applied to improve the UQ accuracy.