Stochastic Tools

Examples

Parameter Studies, Statistics, and Sensitivity Analysis:

• Example 1: Monte Carlo Example

• Example 2: Parameter Study

• Example 3: Parameter Study on a Highly Nonlinear Problem

• Example 4: SOBOL Sensitivity Analysis

Surrogate Models:

• Example 5: Creating a Surrogate Model

• Example 6: Training a Surrogate Model

• Example 7: Evaluating a Surrogate Model

• Example 8: Polynomial Chaos Surrogate

• Example 9: Polynomial Regression Surrogate

• Example 10: POD Reduced Basis Surrogate

• Example 11: Comparison of surrogates using a time-dependent problem

• Example 12: Gaussian Process Surrogate

Performance

The stochastic tools module is optimized in two ways for memory use. First, sub-applications can be executed in batches and all objects utilizing sample data do so using a distributed sample matrix. For further details refer to the following:

• Stochastic Tools Batch Mode

• Distributed Sampling

Objects, Actions, and Syntax

The following is a complete list of all objects available in the stochastic tools module.

Controls

• Stochastic Tools App
• MultiAppCommandLineControlControl for modifying the command line arguments of MultiApps.
• SamplerReceiverControl for receiving data from a Sampler via SamplerParameterTransfer.

Covariance

• Stochastic Tools App
• AddCovarianceActionAdds Covariance objects contained within the [Trainers] and [Surrogates] input blocks.
• ExponentialCovarianceExponential covariance function.
• MaternHalfIntCovarianceMatern half-integer covariance function.
• SquaredExponentialCovarianceSquared Exponential covariance function.

Distributions

• Stochastic Tools App
• JohnsonSBJohnson Special Bounded (SB) distribution.
• JohnsonSBDistributionJohnson Special Bounded (SB) distribution.
• KernelDensity1DKernelDensity1D distribution
• LogisticLogistic distribution.
• LogisticDistributionLogistic distribution.
• LognormalLognormal distribution
• NormalNormal distribution
• NormalDistributionNormal distribution
• TruncatedNormalTruncated normal distribution
• TruncatedNormalDistributionTruncated normal distribution
• UniformContinuous uniform distribution.
• UniformDistributionContinuous uniform distribution.
• WeibullThree-parameter Weibull distribution.
• WeibullDistributionThree-parameter Weibull distribution.

MultiApps

• Stochastic Tools App
• PODFullSolveMultiAppCreates a full-solve type sub-application for each row of a Sampler matrix. On second call, this object creates residuals for a PODReducedBasisTrainer with given basis functions.
• SamplerFullSolveMultiAppCreates a full-solve type sub-application for each row of each Sampler matrix.
• SamplerTransientMultiAppCreates a sub-application for each row of each Sampler matrix.

Outputs

• Stochastic Tools App
• SurrogateTrainerOutputOutput for trained surrogate model data.

Reporters

• Stochastic Tools App
• StatisticsReporterCompute statistical values of a given VectorPostprocessor objects and vectors.
• StochasticReporterStorage container for stochastic simulation results coming from Reporters.

Samplers

• Stochastic Tools App
• CSVSamplerSampler that reads samples from CSV file.
• CartesianProductProvides complete Cartesian product for the supplied variables.
• CartesianProductSamplerProvides complete Cartesian product for the supplied variables.
• LatinHypercubeLatin Hypercube Sampler.
• MonteCarloMonte Carlo Sampler.
• MonteCarloSamplerMonte Carlo Sampler.
• QuadratureQuadrature sampler for Polynomial Chaos.
• QuadratureSamplerQuadrature sampler for Polynomial Chaos.
• SobolSobol variance-based sensitivity analysis Sampler.
• SobolSamplerSobol variance-based sensitivity analysis Sampler.

StochasticTools

• Stochastic Tools App
• StochasticToolsActionAction for performing some common functions for running stochastic simulations.

Surrogates

• Stochastic Tools App
• AddSurrogateActionAdds SurrogateTrainer and SurrogateModel objects contained within the [Trainers] and [Surrogates] input blocks.
• GaussianProcessComputes and evaluates Gaussian Process surrogate model.
• NearestPointSurrogateSurrogate that evaluates the value from the nearest point from data in NearestPointTrainer
• PODReducedBasisSurrogateEvaluates POD-RB surrogate model with reduced operators computed from PODReducedBasisTrainer.
• PolynomialChaosComputes and evaluates polynomial chaos surrogate model.
• PolynomialRegressionSurrogateEvaluates polynomial regression model with coefficients computed from PolynomialRegressionTrainer.

Trainers

• Stochastic Tools App
• AddSurrogateActionAdds SurrogateTrainer and SurrogateModel objects contained within the [Trainers] and [Surrogates] input blocks.
• GaussianProcessTrainerProvides data preperation and training for a Gaussian Process surrogate model.
• NearestPointTrainerLoops over and saves sample values for NearestPointSurrogate.
• PODReducedBasisTrainerComputes the reduced subspace plus the reduced operators for POD-RB surrogate.
• PolynomialChaosTrainerComputes and evaluates polynomial chaos surrogate model.
• PolynomialRegressionTrainerComputes coefficients for polynomial regession model.

Transfers

• Stochastic Tools App
• PODResidualTransferTransfers residual vectors from the sub-application to a a container in the Trainer object.
• PODSamplerSolutionTransferTransfers solution vectors from the sub-applications to a a container in the Trainer object and back.
• SamplerParameterTransferCopies Sampler data to a SamplerReceiver object.
• SamplerPostprocessorTransferTransfers data from Postprocessors on the sub-application to a VectorPostprocessor on the master application.
• SamplerReporterTransferTransfers data from Reporters on the sub-application to a StochasticReporter on the main application.
• SamplerTransferCopies Sampler data to a SamplerReceiver object.

VectorPostprocessors

• Stochastic Tools App
• EvaluateGaussianProcessTool for sampling gaussian process surrogate models.
• EvaluateSurrogateTool for sampling surrogate models.
• GaussianProcessDataTool for extracting hyperparameter data from gaussian process user object and storing in VectorPostprocessor vectors.
• PolynomialChaosDataTool for extracting data from polynomial chaos user object and storing in VectorPostprocessor vectors.
• PolynomialChaosLocalSensitivityTool for calculating local sensitivity with polynomial chaos expansion.
• PolynomialChaosSobolStatisticsCompute SOBOL statistics values of a trained PolynomialChaos surrogate.
• PolynomialChaosStatisticsTool for calculating statistics with polynomial chaos expansion.
• SamplerDataTool for extracting Sampler object data and storing in VectorPostprocessor vectors.
• SobolStatisticsCompute SOBOL statistics values of a given VectorPostprocessor objects and vectors.
• StatisticsCompute statistical values of a given VectorPostprocessor objects and vectors.
• StochasticResultsStorage container for stochastic simulation results coming from a Postprocessor.