Stochastic Tools Module

Examples

Parameter Studies, Statistics, and Sensitivity Analysis:

• Monte Carlo Example

• Parameter Study

• Parameter Study on a Highly Nonlinear Problem

• SOBOL Sensitivity Analysis

Surrogate Models:

• Creating a Surrogate Model

• Training a Surrogate Model

• Evaluating a Surrogate Model

• Polynomial Chaos Surrogate

• Polynomial Regression Surrogate

• POD Reduced Basis Surrogate

• Comparison of surrogates using a time-dependent problem

• Gaussian Process Surrogate

• K-Fold Cross Validation

Bayesian UQ:

• Bayesian Uncertainty Quantification (UQ) on a 1D Diffusion Problem

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

Linking MOOSE with external Machine Learning libraries

The stochastic tools module provides neural network-based surrogate modeling capabilities as well. However, to enable it one needs to compile MOOSE with the C++ APIs of pytorch. For this, follow the appropriate installation guide below:

• Install Stochastic Tools Module with libtorch support

Objects, Actions, and Syntax

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

AuxKernels

• Stochastic Tools App
• SurrogateModelArrayAuxKernelSets a value of a variable based on a surrogate model.
• SurrogateModelAuxKernelSets a value of a variable based on a surrogate model.

AuxScalarKernels

• Stochastic Tools App
• SurrogateModelScalarAuxSets a value of a scalar variable based on a surrogate model.

AuxVariables

Controls

• Stochastic Tools App
• MultiAppCommandLineControlControl for modifying the command line arguments of MultiApps.
• MultiAppSamplerControlControl 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.
• LMCCovariance function for multioutput Gaussian Processes based on the Linear Model of Coregionalization (LMC).
• MaternHalfIntCovarianceMatern half-integer covariance function.
• SquaredExponentialCovarianceSquared Exponential covariance function.

Distributions

• Stochastic Tools App
• BetaBeta distribution
• FDistributionF-distribution or Fisher-Snedecor distribution
• GammaGamma distribution
• JohnsonSBJohnson Special Bounded (SB) distribution.
• JohnsonSBDistributionJohnson Special Bounded (SB) distribution.
• KernelDensity1DKernelDensity1D distribution
• LogisticLogistic distribution.
• LogisticDistributionLogistic distribution.
• LognormalLognormal distribution
• NormalNormal distribution
• NormalDistributionNormal distribution
• StudentTStudent t-distribution
• TruncatedNormalTruncated normal distribution
• TruncatedNormalDistributionTruncated normal distribution
• UniformContinuous uniform distribution.
• UniformDistributionContinuous uniform distribution.
• WeibullThree-parameter Weibull distribution.
• WeibullDistributionThree-parameter Weibull distribution.

Functions

• Stochastic Tools App
• ScaledAbsDifferenceDRLRewardFunctionEvaluates a scaled absolute difference reward function for a process which is controlled by a Deep Reinforcement Learning based surrogate.

Likelihood

• Stochastic Tools App
• AddLikelihoodActionAdds Likelihood objects.
• ExtremeValueGeneralized extreme value likelihood function evaluating the model goodness against experiments.
• GaussianGaussian likelihood function evaluating the model goodness against experiments.
• TruncatedGaussianTruncatedGaussian likelihood function evaluating the model goodness against experiments.

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
• MappingOutputOutput for mapping model data.
• SurrogateTrainerOutputOutput for trained surrogate model data.

ParameterStudy

• Stochastic Tools App
• ParameterStudyActionBuilds objects to set up a basic parameter study.

Postprocessors

• Stochastic Tools App
• AdaptiveSamplingCompletedPostprocessorInforms whether a sampler has finished its sampling (1 = completed, 0 otherwise).

Reporters

• Stochastic Tools App
• ActiveLearningGPDecisionEvaluates a GP surrogate model, determines its prediction quality, launches full model if GP prediction is inadequate, and retrains GP.
• AdaptiveImportanceStatsReporter to compute statistics corresponding to the AdaptiveImportanceSampler.
• AdaptiveMonteCarloDecisionGeneric reporter which decides whether or not to accept a proposed sample in Adaptive Monte Carlo type of algorithms.
• AffineInvariantDifferentialDecisionPerform decision making for Affine Invariant differential MCMC.
• AffineInvariantStretchDecisionPerform decision making for Affine Invariant stretch MCMC.
• BiFidelityActiveLearningGPDecisionPerform active learning decision making in bi-fidelity modeling.
• ConditionalSampleReporterEvaluates parsed function to determine if sample needs to be evaluated, otherwise data is set to a default value.
• CrossValidationScoresTool for extracting cross-validation scores and storing them in a reporter for output.
• DirectPerturbationReporterCompute local sensitivities using the direct perturbation method.
• EvaluateSurrogateTool for sampling surrogate models.
• IndependentMHDecisionPerform decision making for independent Metropolis-Hastings MCMC.
• MappingReporterA reporter which can map full solution fields to a latent space for given variables.
• MorrisReporterCompute global sensitivities using the Morris method.
• PMCMCDecisionGeneric reporter which decides whether or not to accept a proposed sample in parallel Markov chain Monte Carlo type of algorithms.
• ParallelSolutionStorageParallel container to store serialized solution fields from simulations on sub-applications.
• PolynomialChaosReporterTool for extracting data from PolynomialChaos surrogates and computing statistics.
• SingularTripletReporterTool for accessing and outputting the singular triplets of a singular value decomposition in PODMapping.
• SobolReporterCompute SOBOL statistics values of a given VectorPostprocessor or Reporter objects and vectors.
• SolutionContainerClass responsible for collecting distributed solution vectors into a container. We append a new distributed solution vector (containing all variables) at every execution.
• StatisticsReporterCompute statistical values of a given VectorPostprocessor objects and vectors.
• StochasticMatrixTool for extracting Sampler object data and storing data from stochastic simulations.
• StochasticReporterStorage container for stochastic simulation results coming from Reporters.

Samplers

• Stochastic Tools App
• AdaptiveSamplerActionAdds extra objects pertaining to adaptive samplers.
• AISActiveLearningAdaptive Importance Sampler with Gaussian Process Active Learning.
• ActiveLearningMonteCarloSamplerMonte Carlo Sampler for active learning with surrogate model.
• AdaptiveImportanceAdaptive Importance Sampler.
• AffineInvariantDESPerform Affine Invariant Ensemble MCMC with differential sampler.
• AffineInvariantStretchSamplerPerform Affine Invariant Ensemble MCMC with stretch sampler.
• CSVSamplerSampler that reads samples from CSV file.
• Cartesian1DProvides complete Cartesian product for the supplied variables.
• CartesianProductProvides complete Cartesian product for the supplied variables.
• CartesianProductSamplerProvides complete Cartesian product for the supplied variables.
• DirectPerturbationSamplerSampler that creates samples for a direct perturbation-based sensitivity study.
• IndependentGaussianMHPerform M-H MCMC sampling with independent Gaussian propoposals.
• InputMatrixSampler that utilizes a sampling matrix defined at input.
• LatinHypercubeLatin Hypercube Sampler.
• MonteCarloMonte Carlo Sampler.
• MonteCarloSamplerMonte Carlo Sampler.
• MorrisSamplerMorris variance-based sensitivity analysis Sampler.
• NestedMonteCarloMonte Carlo sampler for nested loops of parameters.
• PMCMCBaseParallel Markov chain Monte Carlo base.
• ParallelSubsetSimulationParallel Subset Simulation sampler.
• QuadratureQuadrature sampler for Polynomial Chaos.
• QuadratureSamplerQuadrature sampler for Polynomial Chaos.
• SobolSobol variance-based sensitivity analysis Sampler.
• SobolSamplerSobol variance-based sensitivity analysis Sampler.
• VectorPostprocessorSamplerThe sampler uses vector postprocessors as inputs.

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.
• GaussianProcessSurrogateComputes 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.
• ActiveLearningGaussianProcessPermit re-training Gaussian Process surrogate model for active learning.
• GaussianProcessTrainerProvides data preperation and training for a single- or multi-output 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.
• SerializedSolutionTransferSerializes and transfers solution vectors for given variables from sub-applications.

UserObjects

• Stochastic Tools App
• InverseMappingEvaluates surrogate models and maps the results back to a full solution field for given variables.

VariableMappings

• Stochastic Tools App
• AddVariableMappingActionAdds Mapping objects from a VariableMappings block.
• PODMappingClass which provides a Proper Orthogonal Decomposition-based mapping between full-order and reduced-order spaces.

VectorPostprocessors

• Stochastic Tools App
• GaussianProcessDataTool for extracting hyperparameter data from gaussian process user object and storing in VectorPostprocessor vectors.
• 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.