Study on the effects of the parameters of the Polynomial Chaos method on the error of Leave-One-Out

Abstract

Today, with the development of science and technology, the process of creating new products is shortened thanks to digital simulation technology. One of the effective numerical simulation methods to shorten the simulation time is the Polynomial Chaos (PC) method [1]. With this method, people will choose a small number of samples, calculate on these samples, the remaining results will be interpolated according to the calculation results in the samples, because the measurements in the calculation process have errors. Without knowing the exact result, it is impossible to know whether this error is large or small. Therefore, it is necessary to have an index to evaluate the errors in the calculation process by PC method. This paper presents a method to determine the factors affecting Leave-One-Out (LOO) error of PC method. The simulation results are compared and evaluated with the error between the PC method and the Monte Carlo method (MC).