chaospy 4.1.0

Numerical tool for perfroming uncertainty quantification

Chaospy is a numerical tool for performing uncertainty quantification using polynomial chaos expansions and advanced Monte Carlo methods implemented in Python.

Table of Contents:

• Installation

• Example Usage

• Related Projects

• Questions and Contributions

Installation

Installation should be straight forward:

pip install chaospy

And you should be ready to go.

Example Usage

chaospy is created to be simple and modular. A simple script to implement point collocation method will look as follows:

import numpy
import chaospy

Wrap your code in a function:

coordinates = numpy.linspace(0, 10, 100)
def foo(coordinates, params):
    """Function to do uncertainty quantification on."""
    param_init, param_rate = params
    return param_init*numpy.e**(-param_rate*coordinates)

Construct a multivariate probability distribution:

distribution = chaospy.J(chaospy.Uniform(1, 2), chaospy.Uniform(0.1, 0.2))

Construct polynomial chaos expansion:

polynomial_expansion = chaospy.generate_expansion(8, distribution)

Generate random samples from for example Halton low-discrepancy sequence:

samples = distribution.sample(1000, rule="halton")

Evaluate function for each sample:

evals = numpy.array([foo(coordinates, sample) for sample in samples.T])

Bring the parts together using point collocation method:

foo_approx = chaospy.fit_regression(
    polynomial_expansion, samples, evals)

Derive statistics from model approximation:

expected = chaospy.E(foo_approx, distribution)
deviation = chaospy.Std(foo_approx, distribution)
sobol_main = chaospy.Sens_m(foo_approx, distribution)
sobol_total = chaospy.Sens_t(foo_approx, distribution)

For a more extensive guides on what is going on, see the tutorial collection.

Related Projects

Chaospy is being used in other related projects that requires uncertainty quantification components chaospy provides.

easyVVUQ	Library designed to facilitate verification, validation and uncertainty quantification.
STARFiSh	Shell-based, scientific simulation program for blood flow in mammals.
Profit	Probabilistic response model fitting via interactive tools.
UncertainPy	Uncertainty quantification and sensitivity analysis, tailored towards computational neuroscience.
SparseSpACE	Spatially adaptive combination technique targeted to solve high dimensional numerical integration.

Also a few shout-outs:

OpenTURNS	Thanks to Régis Lebrun for both proposing a collaboration and creating an initial implementation of both Chaospy Compatibility in OpenTURNS and OpenTURNS Compatibility in chaospy.
orthopy quadpy	Thanks to Nico Schlömer for providing the implementation for several of the quadrature integration methods.
UQRF	Thanks to Florian Künzner for providing the initial implementation of kernel density estimation and quantity-of-interest distribution.

Questions and Contributions

Please feel free to file an issue for:

• bug reporting

• asking questions related to usage

• requesting new features

• wanting to contribute with code

If you are using this software in work that will be published, please cite the journal article: Chaospy: An open source tool for designing methods of uncertainty quantification.

And if you use code to deal with stochastic dependencies, please also cite Multivariate Polynomial Chaos Expansions with Dependent Variables.