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

The nonintrusive polynomial chaos expansion method is used to quantify the uncertainty of a stochastic system. It potentially reduces the number of numerical simulations in modeling process, thus improving efficiency while 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. 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 regularization scheme further reduces the number of input samples while maintaining the accuracy of the LARS method.