PolyChaos.jl — A Julia Package for Polynomial Chaos in Systems and Control

摘要

Polynomial chaos expansion (pce) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying mathematical framework to study systems under arbitrary uncertainties of finite variance; we introduce this problem as a so-called mapping under uncertainty. For practical PCE-based applications we require orthogonal polynomials relative to given probability densities, and their quadrature rules. WithPolyChaos.jlwe provide a Julia software package that delivers the desired functionality: given a probability density function,PolyChaos.jloffers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products.PolyChaos.jlis the first PCE-related software written in Julia, a scientific programming language that combines the readability of scripted languages with the speed of compiled languages. We provide illustrating numerical examples that show both PCE andPolyChaos.jlin action.