Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio

Modeling of the evolution of dielectric loss with processing temperature in ferroelectric and dielectric thin oxide films

It was experimentally found that the evolution of dielectric loss with processing temperature displays a common trend in ferroelectric and dielectric thin oxide films: firstly an increase and then a decrease in dielectric loss when the processing temperature is gradually raised. Such a dielectric response of ferroelectric/dielectric thin films has been theoretically addressed in this work. We propose that at the initial stage of the crystallization process in thin films, the transformation from amorphous to crystalline phase should increase substantially the dielectric loss; then, with further increase in the processing temperature, the coalescent growth of small crystalline grains into big ones could be helpful in reducing the dielectric loss by lowering grain boundary densities. The obtained experimental data for (Ba,Sr)TiO3 thin films with 500 nm in thickness were analyzed in terms of the model developed and shown to be in a reasonable agreement with the theoretical results.Comment: The experimentally observed dielectric loss responses in ferroelectric and dielectric thin oxide films have been theoretically addressed in this work, which paves the way for seeking methods in order to tailor the dielectric loss effectively for practical applications. Accepted for publication in Journal of Applied Physic

Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table