An Adaptive Least Angle Regression Method for Uncertainty Quantification in FDTD Computation

Abstract

The non-intrusive polynomial chaos (NIPC) expansion method is used to quantify the uncertainty of a stochastic system. It potentially reduces the number of numerical simulations in modelling process, thus improving efficiency, whilst ensuring accuracy. However, the number of polynomial bases grows substantially with the increase of random parameters, which may render the technique ineffective due to the excessive computational resources. To address such problems, methods based on the sparse strategy such as the least angle regression (LARS) method with hyperbolic index sets can be used. This paper presents the first work to improve the accuracy of the original LARS method for uncertainty quantification (UQ). We propose an adaptive LARS method in order to quantify the uncertainty of the results from the numerical simulations with higher accuracy than the original LARS method. The proposed method outperforms the original LARS method in terms of accuracy and stability. The L2 regularisation scheme further reduces the number of input samples while maintaining the accuracy of the LARS method.Index Terms-Non-intrusive polynomial chaos (NIPC) expansion, least angle regression (LARS), uncertainty quantification (UQ), finite difference time domain (FDTD), Debye media

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

“…9 are satisfactory. The accuracies of using PCA-RR based method for UQ of the FDTD results are therefore 87.5% for average estimation and 72.2% for standard deviation estimation, which outperforms one of the state-of-the-art UQ techniques namely the least angle regression (LARS) method whose accuracies are 86.8% for average estimation and 63.4% for standard deviation estimation [41]. The main causes of unsatisfactory results from the PCA-RR based method include underfitting, outlier and unreasonable ε l .…”

“…The details of utilising the MCM for UQ are explained in [41], where µ(M) and σ(M) 2 are calculated by…”

“…This paper extends a recently developed least angle regression [21], [36]- [40] based UQ method [41] aiming to further reduce the computational cost of UQ for FDTD computation. Our proposed method consists of three stages; sample selection, sparsity process and UQ.…”

“…In statistics, multicollinearity is a phenomenon in which PC bases correlate with one another, with the influence of each PC basis on the UQ results hard to isolate and distinguish [50], [41]. The coefficient estimation for these correlated PC bases is therefore unreliable.…”

“…The main causes of unsatisfactory results from the PCA-RR based method include underfitting, outlier and unreasonable ε l . The underfitting and the outlier have been detailed in our previous work [41]. As for the unreasonable ε l , in the process of the RR method, v is determined at which ε l is minimum.…”