PolyChaos .jl --系统与控制中多项式混沌的Julia软件包
PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control
摘要：
多项式混沌展开（PCE）是一种越来越流行的技术，用于系统和控制中的不确定性传播和量化。基于希尔伯特空间和正交多项式的理论，PCE允许一个统一的数学框架来研究有限方差的任意不确定性下的系统，我们引入这个问题作为一个所谓的映射下的不确定性。对于实际的PCE为基础的应用程序，我们需要正交多项式相对于给定的概率密度，和他们的正交规则。通过PolyChaos，我们提供了一个Julia软件包，它提供了所需的功能：给定概率密度函数，PolyChaos提供了几个数值例程来构建相应的正交多项式，以及求积规则和张量标量积。PolyChaos是第一个用Julia编写的PCE相关软件，Julia是一种科学编程语言，结合了脚本语言的可读性和编译语言的速度。我们提供了说明数值例子，显示PCE和PolyChaos在行动。
英文摘要：
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. With PolyChaos we provide a Julia software package that delivers the desired functionality: given a probability density function, PolyChaos offers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products. PolyChaos is 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 and PolyChaos in action.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
