LatinHypercube

Latin Hypercube Sampler.

Overview

This sampler implements the Latin hypercube strategy presented in McKay et al. (1979) as:

If we wish to ensure also that each of the input variables $var element = document.getElementById("moose-equation-45cf1cad-5b0b-47ad-921b-ec1a912c7fcc");katex.render("X_k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ has all portions of its distribution represented by input values, we can divide the range of each $var element = document.getElementById("moose-equation-cf51ba8e-8ef6-487d-9dc5-d1bbe0ef02dc");katex.render("X_k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ into $var element = document.getElementById("moose-equation-cb3f163d-7b72-4e31-bccd-6097bf6be7a7");katex.render("N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ strata of equal marginal probability $var element = document.getElementById("moose-equation-36e86666-86bc-44fa-a289-8cb8f6047e8d");katex.render("l/N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and sample once from each stratum. Let this sample be $var element = document.getElementById("moose-equation-07a1ad6b-c891-48d8-9630-0b9d97587b2a");katex.render("X_{kj},\\,j=l,\\ldots,N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . These form the $var element = document.getElementById("moose-equation-ed8fde99-230b-432c-b088-e20532445c6d");katex.render("X_k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , component, $var element = document.getElementById("moose-equation-83c5eecf-6266-4b40-a025-b3033ee4e3ce");katex.render("k=l,\\ldots,K", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , in $var element = document.getElementById("moose-equation-9c104b7f-2961-4864-8d76-c4d716195290");katex.render("X_i,\\,i = 1,\\ldots,N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The components of the various $var element = document.getElementById("moose-equation-ce694619-69fc-4ae3-a2e1-6cb07ca92505");katex.render("X_k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 's are matched at random.

Example Input File Syntax

The following input file creates a Latin hypercube sample from two uniform distributions with 10 samples of each distribution.

[Distributions]
  [a]
    type = Uniform
    lower_bound = 100
    upper_bound = 200
  []
  [b]
    type = Uniform
    lower_bound = 10
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'a b'
    num_rows = 10
    seed = 1980
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

The graph in Figure 1 show the Latin hypercube sample generated from the input file snippet where the grid lines are defined with the associated probability based bins.

Figure 1: Latin hypercube sampled data with tick marks defined at the probability intervals.

Input Parameters

distributionsThe distribution names to be sampled, the number of distributions provided defines the number of columns per matrix.
C++ Type:std::vector<DistributionName>
Unit:(no unit assumed)
Controllable:No
Description:The distribution names to be sampled, the number of distributions provided defines the number of columns per matrix.
num_rowsThe size of the square matrix to generate.
C++ Type:unsigned long
Unit:(no unit assumed)
Controllable:No
Description:The size of the square matrix to generate.

Required Parameters

execute_onLINEARThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_MULTIAPP_SETUP
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
limit_get_global_samples429496729The maximum allowed number of items in the DenseMatrix returned by getGlobalSamples method.
Default:429496729
C++ Type:unsigned long
Unit:(no unit assumed)
Controllable:No
Description:The maximum allowed number of items in the DenseMatrix returned by getGlobalSamples method.
limit_get_local_samples429496729The maximum allowed number of items in the DenseMatrix returned by getLocalSamples method.
Default:429496729
C++ Type:unsigned long
Unit:(no unit assumed)
Controllable:No
Description:The maximum allowed number of items in the DenseMatrix returned by getLocalSamples method.
limit_get_next_local_row429496729The maximum allowed number of items in the std::vector returned by getNextLocalRow method.
Default:429496729
C++ Type:unsigned long
Unit:(no unit assumed)
Controllable:No
Description:The maximum allowed number of items in the std::vector returned by getNextLocalRow method.
max_procs_per_row4294967295This will ensure that the sampler is partitioned properly when 'MultiApp/*/max_procs_per_app' is specified. It is not recommended to use otherwise.
Default:4294967295
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:This will ensure that the sampler is partitioned properly when 'MultiApp/*/max_procs_per_app' is specified. It is not recommended to use otherwise.
min_procs_per_row1This will ensure that the sampler is partitioned properly when 'MultiApp/*/min_procs_per_app' is specified. It is not recommended to use otherwise.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:This will ensure that the sampler is partitioned properly when 'MultiApp/*/min_procs_per_app' is specified. It is not recommended to use otherwise.
seed0Random number generator initial seed
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Random number generator initial seed

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/stochastic_tools/test/tests/samplers/latin_hypercube/latin_hypercube.i)
(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc_load.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/surr.i)
(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_main.i)
(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_surr.i)
(modules/stochastic_tools/examples/sobol/main.i)
(modules/stochastic_tools/examples/parameter_study/main.i)
(modules/stochastic_tools/examples/parameter_study/nonlin_diff_react/nonlin_diff_react_parent_normal.i)
(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc.i)
(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_train.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/boundary/trainer.i)
(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_train.i)
(modules/stochastic_tools/examples/parameter_study/nonlin_diff_react/nonlin_diff_react_parent_uniform.i)
(modules/stochastic_tools/examples/parameter_study/main_time.i)
(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/full_order.i)
(modules/combined/examples/stochastic/lhs_uniform.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/trainer.i)
(modules/stochastic_tools/examples/surrogates/cross_validation/all_trainers_uniform_cv.i)
(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_surr.i)
(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_surr.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/boundary/surr.i)
(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/trainer.i)
(modules/stochastic_tools/test/tests/surrogates/nearest_point/np_vec.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/trainer_and_surr.i)
(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc_tuned.i)
(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/surr.i)
(modules/stochastic_tools/test/tests/surrogates/cross_validation/poly_reg_vec.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/errors/trainer_and_surr.i)
(modules/stochastic_tools/test/tests/surrogates/pod_rb/errors/trainer.i)
(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/poly_reg_vec.i)
(modules/stochastic_tools/examples/parameter_study/main_vector.i)

References

Michael D McKay, Richard J Beckman, and William J Conover. Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239–245, 1979.

@article{mckay1979comparison,
    author = "McKay, Michael D and Beckman, Richard J and Conover, William J",
    title = "Comparison of three methods for selecting values of input variables in the analysis of output from a computer code",
    journal = "Technometrics",
    volume = "21",
    number = "2",
    pages = "239--245",
    year = "1979",
    publisher = "Taylor \\& Francis"
}

(modules/stochastic_tools/test/tests/samplers/latin_hypercube/latin_hypercube.i)

[StochasticTools]
[]

[Distributions]
  [a]
    type = Uniform
    lower_bound = 100
    upper_bound = 200
  []
  [b]
    type = Uniform
    lower_bound = 10
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'a b'
    num_rows = 10
    seed = 1980
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[VectorPostprocessors]
  [data]
    type = SamplerData
    sampler = sample
    sampler_method = get_global_samples
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  execute_on = 'INITIAL TIMESTEP_END'
  csv = true
[]

(modules/stochastic_tools/test/tests/samplers/latin_hypercube/latin_hypercube.i)

[StochasticTools]
[]

[Distributions]
  [a]
    type = Uniform
    lower_bound = 100
    upper_bound = 200
  []
  [b]
    type = Uniform
    lower_bound = 10
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'a b'
    num_rows = 10
    seed = 1980
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[VectorPostprocessors]
  [data]
    type = SamplerData
    sampler = sample
    sampler_method = get_global_samples
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  execute_on = 'INITIAL TIMESTEP_END'
  csv = true
[]

(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc_load.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 15.0
    standard_deviation = 2.0
  []
  [bc_dist]
    type = Normal
    mean = 1000.0
    standard_deviation = 100.0
  []
[]

[Samplers]
  [test]
    type = LatinHypercube
    num_rows = 5
    distributions = 'k_dist bc_dist'
    seed = 101
  []
[]

[Reporters]
  [eval_test]
    type = EvaluateSurrogate
    model = mogp
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
    sampler = test
    evaluate_std = true
  []
[]

[Surrogates]
  [mogp]
    type = GaussianProcessSurrogate
    filename = "mogp_lmc_tuned_surr_mogp_trainer.rd"
  []
[]

[VectorPostprocessors]
  [test_params]
    type = SamplerData
    sampler = test
    execute_on = 'final'
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = mogp
    execute_on = final
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = final
    vectorpostprocessors_as_reporters = true
    execute_system_information_on = NONE
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 10
    execute_on = PRE_MULTIAPP_SETUP
    seed = 17
  []
[]

[Surrogates]
  [rbpod]
    type = PODReducedBasisSurrogate
    filename = 'trainer_out_pod_rb.rd'
  []
[]

[VectorPostprocessors]
  [res]
    type = PODSurrogateTester
    model = rbpod
    sampler = sample
    variable_name = "u"
    to_compute = nodal_max
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_main.i)

[StochasticTools]
[]

[Distributions]
  [C_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.02
  []
  [f_dist]
    type = Uniform
    lower_bound = 15
    upper_bound = 25
  []
  [init_dist]
    type = Uniform
    lower_bound = 270
    upper_bound = 330
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 2000
    distributions = 'C_dist f_dist init_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'trans_diff_sub.i'
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = runner
    sampler = hypercube
    param_names = 'Materials/diff_coeff/constant_expressions Functions/src_func/vals Variables/T/initial_condition'
  []
[]

[Transfers]
  [results]
    type = SamplerPostprocessorTransfer
    from_multi_app = runner
    sampler = hypercube
    to_vector_postprocessor = results
    from_postprocessor = 'time_max time_min'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
[]

[Reporters]
  [stats]
    type = StatisticsReporter
    vectorpostprocessors = results
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05'
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_surr.i)

[StochasticTools]
[]

[Distributions]
  [C_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.02
  []
  [f_dist]
    type = Uniform
    lower_bound = 15
    upper_bound = 25
  []
  [init_dist]
    type = Uniform
    lower_bound = 270
    upper_bound = 330
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 100000
    distributions = 'C_dist f_dist init_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[Surrogates]
  [pc_min]
    type = PolynomialChaos
    filename = 'trans_diff_trainer_out_pc_min.rd'
  []
  [pc_max]
    type = PolynomialChaos
    filename = 'trans_diff_trainer_out_pc_max.rd'
  []
  [pr_min]
    type = PolynomialRegressionSurrogate
    filename = 'trans_diff_trainer_out_pr_min.rd'
  []
  [pr_max]
    type = PolynomialRegressionSurrogate
    filename = 'trans_diff_trainer_out_pr_max.rd'
  []
  [np_min]
    type = NearestPointSurrogate
    filename = 'trans_diff_trainer_out_np_min.rd'
  []
  [np_max]
    type = NearestPointSurrogate
    filename = 'trans_diff_trainer_out_np_max.rd'
  []
[]

# Computing statistics
[Reporters]
  [eval_surr]
    type = EvaluateSurrogate
    model = 'pc_max pc_min pr_max pr_min np_max np_min'
    sampler = sample
    parallel_type = ROOT
  []
  [eval_surr_stats]
    type = StatisticsReporter
    reporters = 'eval_surr/pc_max eval_surr/pc_min eval_surr/pr_max eval_surr/pr_min eval_surr/np_max eval_surr/np_min'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/sobol/main.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube_a]
    type = LatinHypercube
    num_rows = 10000
    distributions = 'gamma q_0 T_0 s'
    seed = 2011
  []
  [hypercube_b]
    type = LatinHypercube
    num_rows = 10000
    distributions = 'gamma q_0 T_0 s'
    seed = 2013
  []
  [sobol]
    type = Sobol
    sampler_a = hypercube_a
    sampler_b = hypercube_b
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = sobol
    input_files = 'diffusion.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = sobol
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = sobol
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
  [sobol]
    type = SobolReporter
    sampler = sobol
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/parameter_study/main.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'diffusion.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/parameter_study/nonlin_diff_react/nonlin_diff_react_parent_normal.i)

[StochasticTools]
[]

[Distributions]
  [mu1]
    type = Normal
    mean = 0.3
    standard_deviation = 0.045
  []
  [mu2]
    type = Normal
    mean = 9
    standard_deviation = 1.35
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'mu1 mu2'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'nonlin_diff_react_sub.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Kernels/nonlin_function/mu1 Kernels/nonlin_function/mu2'
  []
  [results]
    type = SamplerPostprocessorTransfer
    from_multi_app = runner
    sampler = hypercube
    to_vector_postprocessor = results
    from_postprocessor = 'max min average'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
[]

[Reporters]
  [stats]
    type = StatisticsReporter
    vectorpostprocessors = results
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05'
  []
[]

[Outputs]
  csv = true
  execute_on = 'FINAL'
[]

(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 15.0
    standard_deviation = 2.0
  []
  [bc_dist]
    type = Normal
    mean = 1000.0
    standard_deviation = 100.0
  []
[]

[Samplers]
  [train]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist bc_dist'
    execute_on = PRE_MULTIAPP_SETUP
    seed = 100
  []
  [test]
    type = LatinHypercube
    num_rows = 5
    distributions = 'k_dist bc_dist'
    seed = 101
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    mode = batch-reset
    sampler = train
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    sampler = train
    param_names = 'Materials/conductivity/prop_values BCs/right/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    sampler = train
    stochastic_reporter = results
    from_reporter = 'T_vec/T'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [eval_test]
    type = EvaluateSurrogate
    model = mogp
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
    sampler = test
    evaluate_std = true
  []
[]

[Trainers]
  [mogp_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'lmc'
    standardize_params = 'true'
    standardize_data = 'true'
    sampler = train
    response_type = vector_real
    response = results/data:T_vec:T
  []
[]

[Covariance]
  [covar]
    type = SquaredExponentialCovariance
    signal_variance = 2.76658083
    noise_variance = 0.0
    length_factor = '3.67866381 2.63421705'
  []
  [lmc]
    type = LMC
    covariance_functions = covar
    num_outputs = 2
    num_latent_funcs = 1
  []
[]

[Surrogates]
  [mogp]
    type = GaussianProcessSurrogate
    trainer = mogp_trainer
  []
[]

[VectorPostprocessors]
  [train_params]
    type = SamplerData
    sampler = train
    execute_on = final
  []
  [test_params]
    type = SamplerData
    sampler = test
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = mogp
    execute_on = final
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = final
    vectorpostprocessors_as_reporters = true
    execute_system_information_on = NONE
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_train.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [L_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.05
  []
  [Tinf_dist]
    type = Uniform
    lower_bound = 290
    upper_bound = 310
  []
[]

[Samplers]
  [pc_sampler]
    type = Quadrature
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [pr_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 6560
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [pc_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pc_sampler
  []
  [pr_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pr_sampler
  []
[]

[Controls]
  [pc_cmdline]
    type = MultiAppSamplerControl
    multi_app = pc_sub
    sampler = pc_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = pr_sub
    sampler = pr_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [pc_data]
    type = SamplerReporterTransfer
    from_multi_app = pc_sub
    sampler = pc_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
  [pr_data]
    type = SamplerReporterTransfer
    from_multi_app = pr_sub
    sampler = pr_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
[]

[Trainers]
  [pc_max]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    sampler = pc_sampler
    response = results/pc_data:max:value
  []
  [pr_max]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    execute_on = timestep_end
    max_degree = 4
    sampler = pr_sampler
    response = results/pr_data:max:value
  []
[]

[Outputs]
  [pc_out]
    type = SurrogateTrainerOutput
    trainers = 'pc_max'
    execute_on = FINAL
  []
  [pr_out]
    type = SurrogateTrainerOutput
    trainers = 'pr_max'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/boundary/trainer.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [Dir_dist]
    type = Uniform
    lower_bound = 0
    upper_bound = 1
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist Dir_dist'
    num_rows = 5
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'Materials/k/prop_values Materials/alpha/prop_values Kernels/source/value BCs/left/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [data]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [mode]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = "pod_rb"
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'u'
    error_res = '1e-9'
    tag_names = 'diff react bodyf dir_src dir_imp'
    tag_types = 'op op src src_dir op_dir'
    execute_on = 'timestep_begin final'
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'pod_rb'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_train.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [q_dist]
    type = Normal
    mean = 10000
    standard_deviation = 500
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
  [Tinf_dist]
    type = Normal
    mean = 300
    standard_deviation = 10
  []
[]

[Samplers]
  [pc_sampler]
    type = Quadrature
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [pr_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 6560
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [pc_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pc_sampler
  []
  [pr_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pr_sampler
  []
[]

[Controls]
  [pc_cmdline]
    type = MultiAppSamplerControl
    multi_app = pc_sub
    sampler = pc_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = pr_sub
    sampler = pr_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [pc_data]
    type = SamplerReporterTransfer
    from_multi_app = pc_sub
    sampler = pc_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
  [pr_data]
    type = SamplerReporterTransfer
    from_multi_app = pr_sub
    sampler = pr_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
[]

[Trainers]
  [pc_max]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    sampler = pc_sampler
    response = results/pc_data:max:value
  []
  [pr_max]
    type = PolynomialRegressionTrainer
    execute_on = timestep_end
    regression_type = "ols"
    max_degree = 4
    sampler = pr_sampler
    response = results/pr_data:max:value
    []
[]

[Outputs]
  [pc_out]
    type = SurrogateTrainerOutput
    trainers = 'pc_max'
    execute_on = FINAL
  []
  [pr_out]
    type = SurrogateTrainerOutput
    trainers = 'pr_max'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/examples/parameter_study/nonlin_diff_react/nonlin_diff_react_parent_uniform.i)

[StochasticTools]
[]

[Distributions]
  [mu1]
    type = Uniform
    lower_bound = 0.21
    upper_bound = 0.39
  []
  [mu2]
    type = Uniform
    lower_bound = 6.3
    upper_bound = 11.7
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'mu1 mu2'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'nonlin_diff_react_sub.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Kernels/nonlin_function/mu1 Kernels/nonlin_function/mu2'
  []
  [results]
    type = SamplerPostprocessorTransfer
    from_multi_app = runner
    sampler = hypercube
    to_vector_postprocessor = results
    from_postprocessor = 'max min average'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
[]

[Reporters]
  [stats]
    type = StatisticsReporter
    vectorpostprocessors = results
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05'
  []
[]

[Outputs]
  csv = true
  execute_on = 'FINAL'
[]

(modules/stochastic_tools/examples/parameter_study/main_time.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerTransientMultiApp
    sampler = hypercube
    input_files = 'diffusion_time.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value T_vec/T'
  []
  [x_transfer]
    type = MultiAppReporterTransfer
    from_multi_app = runner
    subapp_index = 0
    from_reporters = T_vec/x
    to_reporters = const/x
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value results/results:T_vec:T'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
  [const]
    type = ConstantReporter
    real_vector_names = 'x'
    real_vector_values = '0'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.25
[]

[Outputs]
  execute_on = timestep_end
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/full_order.i)

[StochasticTools]
[]

[Distributions]
  [D012_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D3_dist]
    type = Uniform
    lower_bound = 0.15
    upper_bound = 0.6
  []
  [absxs0_dist]
    type = Uniform
    lower_bound = 0.0425
    upper_bound = 0.17
  []
  [absxs1_dist]
    type = Uniform
    lower_bound = 0.065
    upper_bound = 0.26
  []
  [absxs2_dist]
    type = Uniform
    lower_bound = 0.04
    upper_bound = 0.16
  []
  [absxs3_dist]
    type = Uniform
    lower_bound = 0.005
    upper_bound = 0.02
  []
  [src_dist]
    type = Uniform
    lower_bound = 5
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'D012_dist D012_dist D012_dist D3_dist
                     absxs0_dist absxs1_dist absxs2_dist absxs3_dist
                     src_dist src_dist src_dist'
    num_rows = 1000
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [quad]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = sample
    parameters = 'Materials/D0/prop_values
                  Materials/D1/prop_values
                  Materials/D2/prop_values
                  Materials/D3/prop_values
                  Materials/absxs0/prop_values
                  Materials/absxs1/prop_values
                  Materials/absxs2/prop_values
                  Materials/absxs3/prop_values
                  Kernels/src0/value
                  Kernels/src1/value
                  Kernels/src2/value'
    execute_on = 'timestep_begin'
  []
  [results]
    type = SamplerPostprocessorTransfer
    from_multi_app = runner
    sampler = sample
    to_vector_postprocessor = results
    from_postprocessor = 'nodal_l2'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/examples/stochastic/lhs_uniform.i)

[StochasticTools]
[]

[Distributions]
  [cond_inner]
    type = Uniform
    lower_bound = 20
    upper_bound = 30
  []
  [cond_outer]
    type = Uniform
    lower_bound = 90
    upper_bound = 110
  []
  [heat_source]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [alpha_inner]
    type = Uniform
    lower_bound = 1e-6
    upper_bound = 3e-6
  []
  [alpha_outer]
    type = Uniform
    lower_bound = 5e-7
    upper_bound = 1.5e-6
  []
  [ymod_inner]
    type = Uniform
    lower_bound = 2e5
    upper_bound = 2.2e5
  []
  [ymod_outer]
    type = Uniform
    lower_bound = 3e5
    upper_bound = 3.2e5
  []
  [prat_inner]
    type = Uniform
    lower_bound = 0.29
    upper_bound = 0.31
  []
  [prat_outer]
    type = Uniform
    lower_bound = 0.19
    upper_bound = 0.21
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 100000
    distributions = 'cond_inner cond_outer heat_source alpha_inner alpha_outer ymod_inner ymod_outer prat_inner prat_outer'
    execute_on = INITIAL
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = graphite_ring_thermomechanics.i
    sampler = sample
    mode = batch-reset
  []
[]

[Transfers]
  [sub]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'Materials/cond_inner/prop_values Materials/cond_outer/prop_values
                  Postprocessors/heat_source/scale_factor
                  Materials/thermal_strain_inner/thermal_expansion_coeff Materials/thermal_strain_outer/thermal_expansion_coeff
                  Materials/elasticity_tensor_inner/youngs_modulus Materials/elasticity_tensor_outer/youngs_modulus
                  Materials/elasticity_tensor_inner/poissons_ratio Materials/elasticity_tensor_outer/poissons_ratio'
    check_multiapp_execute_on = false
  []
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    sampler = sample
    stochastic_reporter = storage
    from_reporter = 'temp_center_inner/value  temp_center_outer/value  temp_end_inner/value  temp_end_outer/value
                     dispx_center_inner/value dispx_center_outer/value dispx_end_inner/value dispx_end_outer/value
                     dispz_inner/value dispz_outer/value'
  []
[]

[Reporters]
  [storage]
    type = StochasticReporter
    parallel_type = ROOT
  []
  [stats]
    type = StatisticsReporter
    reporters = 'storage/data:temp_center_inner:value  storage/data:temp_center_outer:value  storage/data:temp_end_inner:value  storage/data:temp_end_outer:value
                 storage/data:dispx_center_inner:value storage/data:dispx_center_outer:value storage/data:dispx_end_inner:value storage/data:dispx_end_outer:value
                 storage/data:dispz_inner:value storage/data:dispz_outer:value'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  [out]
    type = JSON
  []
  execute_on = TIMESTEP_END
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/trainer.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 3
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'Materials/k/prop_values Materials/alpha/prop_values Kernels/source/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [snapshots]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [pod_modes]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = "pod_rb"
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'u'
    error_res = '1e-9'
    tag_names = 'diff react bodyf'
    tag_types = 'op op src'
    execute_on = 'timestep_begin final'
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'pod_rb'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/examples/surrogates/cross_validation/all_trainers_uniform_cv.i)

[StochasticTools]
[]

[GlobalParams]
  sampler = cv_sampler
  response = results/response_data:max:value
  cv_type = "k_fold"
  cv_splits = 5
  cv_n_trials = 100
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [L_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.05
  []
  [Tinf_dist]
    type = Uniform
    lower_bound = 290
    upper_bound = 310
  []
[]

[Samplers]
  [cv_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 1000
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [cv_sub]
    type = SamplerFullSolveMultiApp
    input_files = all_sub.i
    mode = batch-reset
  []
[]

[Controls]
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = cv_sub
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [response_data]
    type = SamplerReporterTransfer
    from_multi_app = cv_sub
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [cv_scores]
    type = CrossValidationScores
    models = 'pr_surr pc_surr np_surr gp_surr ann_surr'
    execute_on = FINAL
  []
[]

[Trainers]
  [pr_max]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    max_degree = 3
    cv_surrogate = "pr_surr"
    execute_on = timestep_end
  []
  [pc_max]
    type = PolynomialChaosTrainer
    order = 3
    distributions = "k_dist q_dist L_dist Tinf_dist"
    cv_surrogate = "pc_surr"
    execute_on = timestep_end
  []
  [np_max]
    type = NearestPointTrainer
    cv_surrogate = "np_surr"
    execute_on = timestep_end
  []
  [gp_max]
    type = GaussianProcessTrainer
    covariance_function = 'rbf'
    standardize_params = 'true'
    standardize_data = 'true'
    cv_surrogate = "gp_surr"
    execute_on = timestep_end
  []
  [ann_max]
    type = LibtorchANNTrainer
    num_epochs = 100
    num_batches = 5
    num_neurons_per_layer = '64'
    learning_rate = 1e-2
    rel_loss_tol = 1e-4
    filename = mynet.pt
    read_from_file = false
    print_epoch_loss = 0
    activation_function = 'relu'
    cv_surrogate = "ann_surr"
    standardize_input = false
    standardize_output = false
  []
[]

[Covariance]
  [rbf]
    type = SquaredExponentialCovariance
    noise_variance = 3.79e-6
    signal_variance = 1 #Use a signal variance of 1 in the kernel
    length_factor = '5.34471 1.41191 5.90721 2.83723' #Select a length factor for each parameter
  []
[]

[Surrogates]
  [pr_surr]
    type = PolynomialRegressionSurrogate
    trainer = pr_max
  []
  [pc_surr]
    type = PolynomialChaos
    trainer = pc_max
  []
  [np_surr]
    type = NearestPointSurrogate
    trainer = np_max
  []
  [gp_surr]
    type = GaussianProcessSurrogate
    trainer = gp_max
  []
  [ann_surr]
    type = LibtorchANNSurrogate
    trainer = ann_max
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [q_dist]
    type = Normal
    mean = 10000
    standard_deviation = 500
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
  [Tinf_dist]
    type = Normal
    mean = 300
    standard_deviation = 10
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 100000
    distributions = 'k_dist q_dist L_dist Tinf_dist'
  []
[]

[Surrogates]
  [pc_max]
    type = PolynomialChaos
    filename = 'normal_train_pc_out_pc_max.rd'
  []
  [pr_max]
    type = PolynomialRegressionSurrogate
    filename = 'normal_train_pr_out_pr_max.rd'
  []
[]

[Reporters]
  [pc_max_res]
    type = EvaluateSurrogate
    model = pc_max
    sampler = sample
    parallel_type = ROOT
  []
  [pr_max_res]
    type = EvaluateSurrogate
    model = pr_max
    sampler = sample
    parallel_type = ROOT
  []
  [pr_max_stats]
    type = StatisticsReporter
    reporters = 'pr_max_res/pr_max'
    compute = 'mean stddev'
  []
  [pc_max_stats]
    type = PolynomialChaosReporter
    pc_name = 'pc_max'
    statistics = 'mean stddev'
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = timestep_end
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [L_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.05
  []
  [Tinf_dist]
    type = Uniform
    lower_bound = 290
    upper_bound = 310
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 100000
    distributions = 'k_dist q_dist L_dist Tinf_dist'
  []
[]

[Surrogates]
  [pc_max]
    type = PolynomialChaos
    filename = 'uniform_train_pc_out_pc_max.rd'
  []
  [pr_max]
    type = PolynomialRegressionSurrogate
    filename = 'uniform_train_pr_out_pr_max.rd'
  []
[]

# Computing statistics
[Reporters]
  [pc_max_res]
    type = EvaluateSurrogate
    model = pc_max
    sampler = sample
    parallel_type = ROOT
  []
  [pr_max_res]
    type = EvaluateSurrogate
    model = pr_max
    sampler = sample
    parallel_type = ROOT
  []
  [pr_max_stats]
    type = StatisticsReporter
    reporters = 'pr_max_res/pr_max'
    compute = 'mean stddev'
  []
  [pc_max_stats]
    type = PolynomialChaosReporter
    pc_name = 'pc_max'
    statistics = 'mean stddev'
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = timestep_end
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/boundary/surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [Dir_dist]
    type = Uniform
    lower_bound = 0
    upper_bound = 1
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist Dir_dist'
    num_rows = 10
    execute_on = PRE_MULTIAPP_SETUP
    seed = 17
  []
[]

[Surrogates]
  [rbpod]
    type = PODReducedBasisSurrogate
    filename = 'trainer_out_pod_rb.rd'
  []
[]

[VectorPostprocessors]
  [res]
    type = PODSurrogateTester
    model = rbpod
    sampler = sample
    variable_name = "u"
    to_compute = nodal_max
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/trainer.i)

[StochasticTools]
[]

[Distributions]
  [D012_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D1_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D2_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D3_dist]
    type = Uniform
    lower_bound = 0.15
    upper_bound = 0.6
  []
  [absxs0_dist]
    type = Uniform
    lower_bound = 0.0425
    upper_bound = 0.17
  []
  [absxs1_dist]
    type = Uniform
    lower_bound = 0.065
    upper_bound = 0.26
  []
  [absxs2_dist]
    type = Uniform
    lower_bound = 0.04
    upper_bound = 0.16
  []
  [absxs3_dist]
    type = Uniform
    lower_bound = 0.005
    upper_bound = 0.02
  []
  [src_dist]
    type = Uniform
    lower_bound = 5
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'D012_dist D012_dist D012_dist D3_dist
                     absxs0_dist absxs1_dist absxs2_dist absxs3_dist
                     src_dist src_dist src_dist'
    num_rows = 100
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'Materials/D0/prop_values
                  Materials/D1/prop_values
                  Materials/D2/prop_values
                  Materials/D3/prop_values
                  Materials/absxs0/prop_values
                  Materials/absxs1/prop_values
                  Materials/absxs2/prop_values
                  Materials/absxs3/prop_values
                  Kernels/src0/value
                  Kernels/src1/value
                  Kernels/src2/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [data]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [mode]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'psi'
    error_res = '1e-9'
    tag_names = 'diff0 diff1 diff2 diff3 abs0 abs1 abs2 abs3 src0 src1 src2'
    tag_types = 'op op op op op op op op src src src'
    execute_on = 'timestep_begin final'
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'pod_rb'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/nearest_point/np_vec.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist L_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[GlobalParams]
  sampler = sample
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub_vector.i
    mode = batch-reset
    execute_on = initial
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    param_names = 'Materials/conductivity/prop_values L'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    stochastic_reporter = results
    from_reporter = 'T_vec/T T_vec/x'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [eval]
    type = EvaluateSurrogate
    model = np_surrogate
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
  []
[]

[Trainers]
  [np]
    type = NearestPointTrainer
    response = results/data:T_vec:T
    response_type = vector_real
    execute_on = initial
  []
[]

[Surrogates]
  [np_surrogate]
    type = NearestPointSurrogate
    trainer = np
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = timestep_end
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/internal/trainer_and_surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
[]

[Samplers]
  [train_sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 3
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
  [test_sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 10
    seed = 17
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [quad]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = train_sample
    parameters = 'Materials/k/prop_values Materials/alpha/prop_values Kernels/source/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [data]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [mode]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = train_sample
    trainer_name = "pod_rb"
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'u'
    error_res = '1e-9'
    tag_names = 'diff react bodyf'
    tag_types = 'op op src'
    execute_on = 'timestep_begin final'
  []
[]

[Surrogates]
  [rbpod]
    type = PODReducedBasisSurrogate
    trainer = pod_rb
  []
[]

[VectorPostprocessors]
  [res]
    type = PODSurrogateTester
    model = rbpod
    sampler = test_sample
    variable_name = "u"
    to_compute = nodal_max
    execute_on = 'final'
  []
[]

[Outputs]
  execute_on = 'final'
  csv = true
[]

(modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc_tuned.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 15.0
    standard_deviation = 2.0
  []
  [bc_dist]
    type = Normal
    mean = 1000.0
    standard_deviation = 100.0
  []
[]

[Samplers]
  [train]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist bc_dist'
    execute_on = PRE_MULTIAPP_SETUP
    seed = 100
  []
  [test]
    type = LatinHypercube
    num_rows = 5
    distributions = 'k_dist bc_dist'
    seed = 101
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    mode = batch-reset
    sampler = train
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    sampler = train
    param_names = 'Materials/conductivity/prop_values BCs/right/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    sampler = train
    stochastic_reporter = results
    from_reporter = 'T_vec/T'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [eval_test]
    type = EvaluateSurrogate
    model = mogp
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
    sampler = test
    evaluate_std = true
  []
[]

[Trainers]
  [mogp_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'lmc'
    standardize_params = 'true'
    standardize_data = 'true'
    sampler = train
    response_type = vector_real
    response = results/data:T_vec:T
    tune_parameters = 'lmc:acoeff_0 lmc:lambda_0 covar:signal_variance covar:length_factor'
    tuning_min = '1e-9 1e-9 1e-9 1e-9'
    tuning_max = '1e16 1e16 1e16  1e16'
    num_iters = 1000
    batch_size = 10
    learning_rate = 0.0005
    show_every_nth_iteration = 1
  []
[]

[Covariance]
  [covar]
    type = SquaredExponentialCovariance
    signal_variance = 2.76658083
    noise_variance = 0.0
    length_factor = '3.67866381 2.63421705'
  []
  [lmc]
    type = LMC
    covariance_functions = covar
    num_outputs = 2
    num_latent_funcs = 1
  []
[]

[Surrogates]
  [mogp]
    type = GaussianProcessSurrogate
    trainer = mogp_trainer
  []
[]

[VectorPostprocessors]
  [train_params]
    type = SamplerData
    sampler = train
    execute_on = final
  []
  [test_params]
    type = SamplerData
    sampler = test
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = mogp
    execute_on = final
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = final
    vectorpostprocessors_as_reporters = true
    execute_system_information_on = NONE
  []
  [surr]
    type = SurrogateTrainerOutput
    execute_on = FINAL
    trainers = "mogp_trainer"
  []
[]

(modules/stochastic_tools/examples/surrogates/pod_rb/2d_multireg/surr.i)

[StochasticTools]
[]

[Distributions]
  [D012_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D1_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D2_dist]
    type = Uniform
    lower_bound = 0.2
    upper_bound = 0.8
  []
  [D3_dist]
    type = Uniform
    lower_bound = 0.15
    upper_bound = 0.6
  []
  [absxs0_dist]
    type = Uniform
    lower_bound = 0.0425
    upper_bound = 0.17
  []
  [absxs1_dist]
    type = Uniform
    lower_bound = 0.065
    upper_bound = 0.26
  []
  [absxs2_dist]
    type = Uniform
    lower_bound = 0.04
    upper_bound = 0.16
  []
  [absxs3_dist]
    type = Uniform
    lower_bound = 0.005
    upper_bound = 0.02
  []
  [src_dist]
    type = Uniform
    lower_bound = 5
    upper_bound = 20
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'D012_dist D012_dist D012_dist D3_dist
                     absxs0_dist absxs1_dist absxs2_dist absxs3_dist
                     src_dist src_dist src_dist'
    num_rows = 1000
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[Surrogates]
  [rbpod]
    type = PODReducedBasisSurrogate
    filename = 'trainer_out_pod_rb.rd'
    change_rank = 'psi'
    new_ranks = '40'
  []
[]

[VectorPostprocessors]
  [res]
    type = PODSurrogateTester
    model = rbpod
    sampler = sample
    variable_name = 'psi'
    to_compute = nodal_l2
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/test/tests/surrogates/cross_validation/poly_reg_vec.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist L_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[GlobalParams]
  sampler = sample
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub_vector.i
    mode = batch-reset
    execute_on = initial
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    param_names = 'Materials/conductivity/prop_values L'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    stochastic_reporter = results
    from_reporter = 'T_vec/T T_vec/x'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [cv_scores]
    type = CrossValidationScores
    models = pr_surrogate
    execute_on = FINAL
  []
[]

[Trainers]
  [pr_trainer]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = results/data:T_vec:T
    response_type = vector_real
    execute_on = timestep_end
    max_degree = 1
    cv_type = "k_fold"
    cv_splits = 2
    cv_n_trials = 3
    cv_surrogate = pr_surrogate
    cv_seed = 1
  []
[]

[Surrogates]
  [pr_surrogate]
    type = PolynomialRegressionSurrogate
    trainer = pr_trainer
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/errors/trainer_and_surr.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
[]

[Samplers]
  [train_sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 3
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
  [test_sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 10
    seed = 17
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [quad]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = train_sample
    parameters = 'Materials/k/prop_values Materials/alpha/prop_values Kernels/source/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [data]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [mode]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = train_sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = train_sample
    trainer_name = "pod_rb"
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'u'
    error_res = '1e-9'
    tag_names = 'diff react bodyf'
    tag_types = 'op op src'
    execute_on = 'timestep_begin final'
  []
[]

[Surrogates]
  [rbpod]
    type = PODReducedBasisSurrogate
    trainer = pod_rb
  []
[]

[VectorPostprocessors]
  [res]
    type = PODSurrogateTester
    model = rbpod
    sampler = test_sample
    variable_name = "u"
    to_compute = nodal_max
    execute_on = 'final'
  []
[]

(modules/stochastic_tools/test/tests/surrogates/pod_rb/errors/trainer.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [alpha_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
  [S_dist]
    type = Uniform
    lower_bound = 2.5
    upper_bound = 7.5
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    distributions = 'k_dist alpha_dist S_dist'
    num_rows = 3
    execute_on = PRE_MULTIAPP_SETUP
    max_procs_per_row = 1
  []
[]

[MultiApps]
  [sub]
    type = PODFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin final'
    max_procs_per_app = 1
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'Materials/k/prop_values Materials/alpha/prop_values Kernels/source/value'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [snapshot]
    type = PODSamplerSolutionTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'timestep_begin'
    check_multiapp_execute_on = false
  []
  [mode]
    type = PODSamplerSolutionTransfer
    to_multi_app = sub
    sampler = sample
    trainer_name = 'pod_rb'
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
  [res]
    type = PODResidualTransfer
    from_multi_app = sub
    sampler = sample
    trainer_name = "pod_rb"
    execute_on = 'final'
    check_multiapp_execute_on = false
  []
[]

[Trainers]
  [pod_rb]
    type = PODReducedBasisTrainer
    var_names = 'u'
    error_res = '1e-9'
    tag_names = 'diff react bodyf'
    tag_types = 'op op src'
    execute_on = 'timestep_begin final'
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'pod_rb'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/poly_reg_vec.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist L_dist'
    execute_on = PRE_MULTIAPP_SETUP
    min_procs_per_row = 2
  []
[]

[GlobalParams]
  sampler = sample
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub_vector.i
    mode = batch-reset
    execute_on = initial
    min_procs_per_app = 2
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    param_names = 'Materials/conductivity/prop_values L'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    stochastic_reporter = results
    from_reporter = 'T_vec/T T_vec/x'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [eval]
    type = EvaluateSurrogate
    model = pr_surrogate
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
  []
[]

[Trainers]
  [pr]
    type = PolynomialRegressionTrainer
    regression_type = ols
    max_degree = 2
    response = results/data:T_vec:T
    response_type = vector_real
    execute_on = initial
  []
[]

[Surrogates]
  [pr_surrogate]
    type = PolynomialRegressionSurrogate
    trainer = pr
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = timestep_end
  []
[]

(modules/stochastic_tools/examples/parameter_study/main_vector.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'diffusion_vector.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'acc/T_avg:value acc/q_left:value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:acc:T_avg:value results/results:acc:q_left:value'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files
References