论文标题
POCET：MATLAB的多项式混乱扩展工具箱
PoCET: a Polynomial Chaos Expansion Toolbox for Matlab
论文作者
论文摘要
我们介绍了POCET：用于MATLAB的免费和开放式多项式混乱扩展工具箱，该工具箱具有用于线性和非线性动态系统的自动生成多项式混乱扩展（PCE），具有时间不变的随机随机参数或初始条件，以及几个模拟工具。它提供了高斯，统一和β概率密度函数，基于PCE系数的投影和搭配计算的内置处理，以及从PCE计算的随机矩。为了提高其适用性，已经设计了用于计算相关积分的有效算法。 POCET带有各种介绍性和启发性的例子。在整个论文中，我们展示了如何使用Pocet在简单的普通微分方程上执行多项式混乱的扩展，以及如何使用它来解决最佳实验设计的更复杂的任务。
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.
