pyStatReduce

Python package for stochastic dimension reduction based on nonlinearity of a quantity of interest. This package uses stochastic collocation to estimate statistical moments of a quantity of interest (QoI).

Dependencies

Besides Numpy and SciPy, this package depends on another python package called chaospy, which can be installed using

pip install chaospy==2.3.5

The documentation of chaospy can be found at the following link

http://chaospy.readthedocs.io/en/master/

Major Classes

Using pyStatReduce for approximating statistics involves working with objects of the following major classes and their subclasses

• QuantityOfInterest : Base class for creating subclasses for a specific quantity of interest. examples of subclasses of QuantityOfInterest can be found in src/examples directory
• StochasticCollocation : Base class that handles uncertainty propagation using stochastic collocation. This is designed to handle multivariate uniform or normal distributions.
• Dist : Base class in chaospy upon different distributions have been defined. see here for a complete list of available distributions.
• DimensionReduction : Base class that identifies the directions with highest nonlinearity in the QoI. This is done by computing the dominant eigenmodes of the Hessian of the QoI in the isoprobabilistic space.

Sample script

A sample script for using the package has been provided below. However, the user is recommended to look in the test to see the latest API for the package

systemsize = 4
eigen_decayrate = 2.0

# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)

# Create stochastic collocation object
collocation = StochasticCollocation(3, "Normal")

# Create dimension reduction object
threshold_factor = 0.9
dominant_space = DimensionReduction(threshold_factor)

# Initialize chaospy distribution
std_dev = 0.2*np.ones(QoI.systemsize)
x = np.ones(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))

# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space.getDominantDirections(QoI, jdist)

mu_j = collocation.normalReduced(QoI, jdist, dominant_space)