PoCET：一种Matlab的多项式混沌展开算法
PoCET: a Polynomial Chaos Expansion Toolbox for Matlab
摘要：
我们介绍PoCET：一个自由开放的Polynomial Chaos Expansion工具，用于Matlab，具有自动生成线性和非线性动态系统的多项式混沌展开（PCE），具有时不变随机参数或初始条件，以及几个仿真工具。它提供了一个内置的处理高斯，均匀和β概率密度函数，投影和配置为基础的计算PCE系数，并计算随机矩从PCE。为了提高其适用性，设计了计算所涉及积分的有效算法。PoCET附带了各种介绍性和指导性的示例。在本文中，我们展示了如何使用PoCET对一个简单的常微分方程进行多项式混沌展开，以及如何将其用于解决更复杂的优化实验设计任务。
英文摘要：
We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions, as well as several simulation tools. It offers a built-in handling of Gaussian, uniform, and beta probability density functions, projection and collocation-based calculation of PCE coefficients, and the calculation of stochastic moments from a PCE. Efficient algorithms for the calculation of the involved integrals have been designed in order to increase its applicability. PoCET comes with a variety of introductory and instructive examples. Throughout the paper we show how to perform a polynomial chaos expansion on a simple ordinary differential equation using PoCET, as well as how it can be used to solve the more complex task of optimal experimental design.
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。
