EvaluateGaussianProcess

Tool for sampling gaussian process surrogate models.

Overview

Similar in function to EvaluateSurrogate, this object takes in a sampler and a GaussianProcess surrogate model and executes the evaluate method within each surrogate for each row of the sampler. The evaluate return the predictive mean and standard deviation of the Gaussian process surrogate at the specified evaluation point.

Example Syntax

Simple example using EvaluateGaussianProcess

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[VectorPostprocessors]
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []

[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    filename = 'gauss_process_training_GP_avg_trainer.rd'
  []
[]

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

CSV output when output_samples = true, note the predictive standard deviation in the last column.

surrogate,sample_p0,sample_p1,sample_p2
GP_avg,sample_p0,sample_p1,GP_avg_std
680.81518263199,8.1474396732963,9319.6492446266,0.58627430888001
1101.357289321,4.5170853933506,10872.970311667,0.58627427931307
787.59042890478,6.9085650921783,10118.299854788,0.58627437370922
722.81295049602,7.2617914444642,9222.6647540836,0.58627431013298
1127.8161258388,4.2903122598679,10668.108638239,0.58627425407458
1602.4960766395,2.7392312254796,10716.920553975,0.58627406227184
...

Input Parameters

modelName of surrogate models.
C++ Type:std::vector<UserObjectName>
Options:
Description:Name of surrogate models.
samplerSampler to use for evaluating surrogate models.
C++ Type:SamplerName
Options:
Description:Sampler to use for evaluating surrogate models.

Required Parameters

contains_complete_historyFalseSet this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
Default:False
C++ Type:bool
Options:
Description:Set this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
output_samplesFalseTrue to output value of parameter values from samples (this may be VERY large).
Default:False
C++ Type:bool
Options:
Description:True to output value of parameter values from samples (this may be VERY large).
parallel_typeREPLICATEDSet how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is preformed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
Default:REPLICATED
C++ Type:MooseEnum
Options:DISTRIBUTED, REPLICATED
Description:Set how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is preformed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
force_preauxFalseForces the GeneralUserObject to be executed in PREAUX
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREAUX
force_preicFalseForces the GeneralUserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREIC during initial setup
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_2D_tuned.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_testing.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_Matern_half_int.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_exponential_tuned.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_Matern_half_int_tuned.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_tuned.i)
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_exponential.i)
(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_1D_tuned.i)
(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_1D.i)
(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_2D.i)

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_testing.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[VectorPostprocessors]
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []

[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    filename = 'gauss_process_training_GP_avg_trainer.rd'
  []
[]


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

(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_2D_tuned.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 50
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [cart_sample]
    type = CartesianProduct
    linear_space_items = '1 0.09 100
                          9000 20 100 '
    execute_on = initial
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    multi_app = sub
    sampler = train_sample
    stochastic_reporter = results
    from_reporter = 'avg/value'
  []
[]

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


[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'rbf'
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    tao_options = '-tao_bncg_type kd'
    sampler = train_sample
    response = results/data:avg:value
    tune_parameters = ' signal_variance length_factor'
    tuning_min = ' 1e-9 1e-9'
    tuning_max = ' 1e16  1e16'
  []
[]


[Covariance]
  [rbf]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971 0.38971'         #Select a length factor for each parameter (k and q)
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = 'GP_avg_trainer'
  []
[]

[VectorPostprocessors]
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [cart_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = cart_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_testing.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[VectorPostprocessors]
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []

[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    filename = 'gauss_process_training_GP_avg_trainer.rd'
  []
[]


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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_Matern_half_int.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'   #Choose a Matern with half-integer argument for the kernel
    standardize_params = 'true'           #Center and scale the training params
    standardize_data = 'true'             #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=MaternHalfIntCovariance
    p = 2                                 #Define the exponential factor
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-6                     #A small amount of noise can help with numerical stability
    length_factor = '0.551133 0.551133'       #Select a length factor for each parameter (k and q)
  []
[]

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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'             #Choose a squared exponential for the kernel
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-6                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971 0.38971'         #Select a length factor for each parameter (k and q)
  []
[]


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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_exponential_tuned.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'           #Choose an exponential for the kernel
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
    tao_options = '-tao_bncg_type ssml_bfgs'
    tune_parameters = 'signal_variance length_factor'
    tuning_min = ' 1e-9 1e-9'
    tuning_max = ' 1e16  1e16'
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=ExponentialCovariance
    gamma = 2                                 #Define the exponential factor
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.551133 0.551133'       #Select a length factor for each parameter (k and q)
  []
[]

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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_Matern_half_int_tuned.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'   #Choose a Matern with half-integer argument for the kernel
    standardize_params = 'true'           #Center and scale the training params
    standardize_data = 'true'             #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
    tao_options = '-tao_bncg_type ssml_bfgs'
    tune_parameters = ' signal_variance length_factor'
    tuning_min = ' 1e-9 1e-9'
    tuning_max = ' 1e16  1e16'
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=MaternHalfIntCovariance
    p = 2                                 #Define the exponential factor
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.551133 0.551133'       #Select a length factor for each parameter (k and q)
  []
[]

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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_tuned.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'             #Choose a squared exponential for the kernel
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
    tao_options = '-tao_bncg_type ssml_bfgs'
    tune_parameters = ' signal_variance length_factor'
    tuning_min = ' 1e-9 1e-9'
    tuning_max = ' 1e16  1e16'
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971 0.38971'         #Select a length factor for each parameter (k and q)
  []
[]


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

(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_exponential.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [test_sample]
    type = MonteCarlo
    num_rows = 100
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerPostprocessorTransfer
    multi_app = sub
    sampler = train_sample
    to_vector_postprocessor = results
    from_postprocessor = 'avg'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samp_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = test_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'covar'           #Choose an exponential for the kernel
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = GP_avg_trainer
  []
[]

[Covariance]
  [covar]
    type=ExponentialCovariance
    gamma = 1                                 #Define the exponential factor
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-6                     #A small amount of noise can help with numerical stability
    length_factor = '0.551133 0.551133'       #Select a length factor for each parameter (k and q)
  []
[]

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

(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_1D_tuned.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]
  [train_sample]
    type = MonteCarlo
    num_rows = 6
    distributions = 'q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [cart_sample]
    type = CartesianProduct
    linear_space_items = '9000 20 100'
    execute_on = initial
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    multi_app = sub
    sampler = train_sample
    stochastic_reporter = results
    from_reporter = 'avg/value'
  []
[]

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

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'rbf'
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg:value
    tao_options = '-tao_bncg_type kd'
    tune_parameters = ' signal_variance length_factor'
    tuning_min = ' 1e-9 1e-9'
    tuning_max = ' 1e16  1e16'
  []
[]

[Covariance]
  [rbf]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971'         #Select a length factor for each parameter (k and q)
  []
[]

[Surrogates]
  [gauss_process_avg]
    type = GaussianProcess
    trainer = 'GP_avg_trainer'
  []
[]

# # Computing statistics
[VectorPostprocessors]
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'gauss_process_avg'
    execute_on = final
  []
  [cart_avg]
    type = EvaluateGaussianProcess
    model = gauss_process_avg
    sampler = cart_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = gauss_process_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
[]


[Outputs]
  csv = true
  execute_on = FINAL
[]

(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_1D.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]
  [train_sample]
    type = MonteCarlo
    num_rows = 6
    distributions = 'q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [cart_sample]
    type = CartesianProduct
    linear_space_items = '9000 20 100'
    execute_on = initial
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    multi_app = sub
    sampler = train_sample
    stochastic_reporter = results
    from_reporter = 'avg/value'
  []
[]

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

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    sampler = train_sample
    response = results/data:avg:value
    covariance_function = 'rbf'
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
  []
[]

[Covariance]
  [rbf]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-3                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971'         #Select a length factor for each parameter (k and q)
  []
[]

[Surrogates]
  [gauss_process_avg]
    type = GaussianProcess
    trainer = 'GP_avg_trainer'
  []
[]

# # Computing statistics
[VectorPostprocessors]
  [cart_avg]
    type = EvaluateGaussianProcess
    model = gauss_process_avg
    sampler = cart_sample
    output_samples = true
    execute_on = final
  []
  [train_avg]
    type = EvaluateGaussianProcess
    model = gauss_process_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
[]


[Outputs]
  csv = true
  execute_on = FINAL
[]

(modules/stochastic_tools/examples/surrogates/gaussian_process/gaussian_process_uniform_2D.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
[]

[Samplers]
  [train_sample]
    type = MonteCarlo
    num_rows = 50
    distributions = 'k_dist q_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [cart_sample]
    type = CartesianProduct
    linear_space_items = '1 0.09 100
                          9000 20 100 '
    execute_on = initial
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = train_sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppCommandLineControl
    multi_app = sub
    sampler = train_sample
    param_names = 'Materials/conductivity/prop_values Kernels/source/value'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    multi_app = sub
    sampler = train_sample
    stochastic_reporter = results
    from_reporter = 'avg/value'
  []
[]

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

[Trainers]
  [GP_avg_trainer]
    type = GaussianProcessTrainer
    execute_on = timestep_end
    covariance_function = 'rbf'
    standardize_params = 'true'               #Center and scale the training params
    standardize_data = 'true'                 #Center and scale the training data
    sampler = train_sample
    response = results/data:avg:value
  []
[]


[Covariance]
  [rbf]
    type=SquaredExponentialCovariance
    signal_variance = 1                       #Use a signal variance of 1 in the kernel
    noise_variance = 1e-6                     #A small amount of noise can help with numerical stability
    length_factor = '0.38971 0.38971'         #Select a length factor for each parameter (k and q)
  []
[]

[Surrogates]
  [GP_avg]
    type = GaussianProcess
    trainer = 'GP_avg_trainer'
  []
[]

[VectorPostprocessors]
  [train_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = train_sample
    output_samples = true
    execute_on = final
  []
  [cart_avg]
    type = EvaluateGaussianProcess
    model = GP_avg
    sampler = cart_sample
    output_samples = true
    execute_on = final
  []
  [hyperparams]
    type = GaussianProcessData
    gp_name = 'GP_avg'
    execute_on = final
  []
[]

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

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