PoCET: a Polynomial Chaos Expansion Toolbox for Matlab

TL;DR

PoCET is an open-source MATLAB toolbox that automates polynomial chaos expansion for dynamic systems with stochastic parameters, providing efficient algorithms and practical examples for analysis and optimal experimental design.

Contribution

It introduces a comprehensive MATLAB toolbox with automatic PCE generation, efficient algorithms, and diverse simulation tools for stochastic dynamic systems.

Findings

Successfully applied PCE to a simple ODE example.

Demonstrated PCE's use in optimal experimental design.

Provided accessible examples for users.

Abstract

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.