论文标题
polychaos.jl-系统和控制中多项式混乱的朱莉娅包装
PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control
论文作者
论文摘要
多项式混乱扩展（PCE）是系统和控制中不确定性传播和量化的越来越流行的技术。基于希尔伯特空间和正交多项式的理论，PCE允许在有限差异的任意不确定性下进行统一的数学框架来研究系统；我们将这个问题介绍为在不确定性下的所谓映射。对于基于PCE的实用应用，我们需要相对于给定的概率密度及其正交规则的正交多项式。使用Polychaos，我们提供了提供所需功能的Julia软件包：鉴于概率密度函数，PolyChaos提供了几个数值例程来构建各自的正交多项式，以及正交规则以及张开的标量产品。 PolyChaos是第一个用Julia编写的PCE相关软件，该软件是一种科学的编程语言，将脚本语言的可读性与编译语言的速度相结合。我们提供说明的数值示例，这些示例显示了PCE和多cha的作用。
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.
