PolynomialChaosSobolStatistics

Compute SOBOL statistics values of a trained PolynomialChaos surrogate.

Overview

This object computes Sobol sensitivity indices based on a trained PolynomialChaos surrogate model. The alogrithm is based on computations described in Sudret (2008). The sensitivities to be computed are defined by the input parameter "sensitivity_order": first computes first-order sensitivities, second computes second-order sensitivities, all computes all sensitivities (replacing first and second), and total comutes the total sensitivities.

Example Syntax

The following input snippet uses the GFunction test object, which is defined as:

var element = document.getElementById("moose-equation-5abf8d97-8757-490d-8b49-bca8ffddbf65");katex.render("g(x_1, x_2, \\ldots, x_n) = \\prod_{i=1}^n\\frac{|4x_i-2|+q_i}{1+q_i},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});

where $var element = document.getElementById("moose-equation-f8570cc4-e6a6-4be1-af13-f71ab8c25141");katex.render("\\vec{q}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is defined in the input file, $var element = document.getElementById("moose-equation-48673fb9-5e6e-488d-acb9-3243a05d1271");katex.render("x", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the vector of model data, and $var element = document.getElementById("moose-equation-e143abf5-f332-433c-8b64-e73f67e98826");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the number of input variables. The $var element = document.getElementById("moose-equation-1dbabf76-a35c-46a0-af44-a2d70a98fa59");katex.render("x", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ data is generated by QuadratureSampler object.

[VectorPostprocessors]
  [results]
    type = GFunction
    sampler = sample
    q_vector = '0 0.5 3 9 99 99'
    execute_on = INITIAL
    outputs = none
  []
  [sobol]
    type = PolynomialChaosSobolStatistics
    pc_name = poly_chaos
    sensitivity_order = 'all total'
    execute_on = timestep_end
  []
[]

Example Output

The resulting output contains a single column of all the sensitivities and columnes containing the indicies. The column i_T is the total sensitivity index, i_1 is the first index, i_2 second, and so on to i_n. For sensitivity orders less than $var element = document.getElementById("moose-equation-93e7faff-54ea-4828-9ad4-0a061480e9d5");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , the last index is repeated and can be ignored.

poly_chaos,i_T,i_1,i_2,i_3,i_4,i_5,i_6
0.66924780365628,0,0,0,0,0,0,0
0.28619846733258,1,0,0,0,0,0,0
0.038392996228437,2,0,0,0,0,0,0
0.0060411077026529,3,0,0,0,0,0,0
5.9812540024784e-05,4,0,0,0,0,0,0
5.9812540024784e-05,5,0,0,0,0,0,0
0.66924780365628,0,0,0,0,0,0,0
0.28619846733258,0,1,1,1,1,1,1
0.038392996228437,0,2,2,2,2,2,2
0.0060411077026529,0,3,3,3,3,3,3
5.9812540024784e-05,0,4,4,4,4,4,4
5.9812540024784e-05,0,5,5,5,5,5,5
5.285967493225e-29,0,0,1,1,1,1,1
4.830441079516e-30,0,0,2,2,2,2,2
2.3537404069876e-31,0,0,3,3,3,3,3
1.2851971453103e-31,0,0,4,4,4,4,4
9.7243393783398e-32,0,0,5,5,5,5,5
2.8036255956726e-31,0,1,2,2,2,2,2
5.6458324345948e-32,0,1,3,3,3,3,3
5.201235192063e-32,0,1,4,4,4,4,4
3.8229032758747e-32,0,1,5,5,5,5,5
3.6702787303277e-33,0,2,3,3,3,3,3
6.8822775950545e-33,0,2,4,4,4,4,4
5.0863886742273e-33,0,2,5,5,5,5,5
9.4052217449154e-34,0,3,4,4,4,4,4
8.2525733364501e-34,0,3,5,5,5,5,5
1.1437129538783e-35,0,4,5,5,5,5,5
8.3110407141877e-33,0,0,1,2,2,2,2
4.3564024206612e-35,0,0,1,3,3,3,3
2.2616474877005e-35,0,0,1,4,4,4,4
0,0,0,1,5,5,5,5
6.0559817026029e-37,0,0,2,3,3,3,3
4.9864238916151e-35,0,0,2,4,4,4,4
1.2773220117863e-35,0,0,2,5,5,5,5
2.2616474877005e-35,0,0,3,4,4,4,4
2.2462790842028e-36,0,0,3,5,5,5,5
3.6186359803208e-36,0,0,4,5,5,5,5
8.4742207610772e-36,0,1,2,3,3,3,3
4.9864238916151e-35,0,1,2,4,4,4,4
6.5128801849667e-37,0,1,2,5,5,5,5
6.0559817026029e-37,0,1,3,4,4,4,4
4.7849731971184e-37,0,1,3,5,5,5,5
1.1995661973331e-36,0,1,4,5,5,5,5
1.137261858829e-36,0,2,3,4,4,4,4
1.3291592214218e-38,0,2,3,5,5,5,5
5.615697710507e-37,0,2,4,5,5,5,5
2.0768112834715e-36,0,3,4,5,5,5,5
0,0,0,1,2,3,3,3
0,0,0,1,2,4,4,4
0,0,0,1,2,5,5,5
0,0,0,1,3,4,4,4
0,0,0,1,3,5,5,5
0,0,0,1,4,5,5,5
0,0,0,2,3,4,4,4
0,0,0,2,3,5,5,5
0,0,0,2,4,5,5,5
0,0,0,3,4,5,5,5
0,0,1,2,3,4,4,4
0,0,1,2,3,5,5,5
0,0,1,2,4,5,5,5
0,0,1,3,4,5,5,5
0,0,2,3,4,5,5,5
0,0,0,1,2,3,4,4
0,0,0,1,2,3,5,5
0,0,0,1,2,4,5,5
0,0,0,1,3,4,5,5
0,0,0,2,3,4,5,5
0,0,1,2,3,4,5,5
0,0,0,1,2,3,4,5

Input Parameters

pc_nameName of PolynomialChaos.
C++ Type:std::vector<UserObjectName>
Options:
Description:Name of PolynomialChaos.
sensitivity_orderOrder of sensitivities to compute. The all option computes all possible orders.
C++ Type:MultiMooseEnum
Options:first, second, all, total
Description:Order of sensitivities to compute. The all option computes all possible orders.

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.
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.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Options:
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

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_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Options:
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Options:
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Options:
Description:Forces the UserObject 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/poly_chaos_normal.i)
(modules/stochastic_tools/examples/surrogates/poly_chaos_uniform.i)
(modules/stochastic_tools/test/tests/surrogates/poly_chaos/sobol.i)
(modules/combined/examples/stochastic/poly_chaos_uniform.i)

References

Bruno Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93(7):964–979, 2008. Bayesian Networks in Dependability. doi:10.1016/j.ress.2007.04.002.

@article{sudret2008global,
    author = "Sudret, Bruno",
    title = "Global sensitivity analysis using polynomial chaos expansions",
    journal = "Reliability Engineering \& System Safety",
    volume = "93",
    number = "7",
    pages = "964--979",
    year = "2008",
    note = "Bayesian Networks in Dependability",
    doi = "10.1016/j.ress.2007.04.002"
}

(modules/stochastic_tools/test/tests/surrogates/poly_chaos/sobol.i)

[StochasticTools]
[]

[Distributions/uniform]
  type = Uniform
  lower_bound = 0
  upper_bound = 1
[]

[Samplers/sample]
  type = Quadrature
  order = 4
  distributions = 'uniform uniform uniform uniform uniform uniform'
  execute_on = 'initial'
[]

[VectorPostprocessors]
  [results]
    type = GFunction
    sampler = sample
    q_vector = '0 0.5 3 9 99 99'
    execute_on = INITIAL
    outputs = none
  []
  [sobol]
    type = PolynomialChaosSobolStatistics
    pc_name = poly_chaos
    sensitivity_order = 'all total'
    execute_on = timestep_end
  []
[]

[Surrogates]
  [poly_chaos]
    type = PolynomialChaos
    trainer = poly_chaos
  []
[]

[Trainers]
  [poly_chaos]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 4
    distributions = 'uniform uniform uniform uniform uniform uniform'
    sampler = sample
    response = results/g_values
  []
[]

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

(modules/stochastic_tools/test/tests/surrogates/poly_chaos/gold/sobol_out_sobol_0002.csv)

poly_chaos,i_T,i_1,i_2,i_3,i_4,i_5,i_6
0.66924780365628,0,0,0,0,0,0,0
0.28619846733258,1,0,0,0,0,0,0
0.038392996228437,2,0,0,0,0,0,0
0.0060411077026529,3,0,0,0,0,0,0
5.9812540024784e-05,4,0,0,0,0,0,0
5.9812540024784e-05,5,0,0,0,0,0,0
0.66924780365628,0,0,0,0,0,0,0
0.28619846733258,0,1,1,1,1,1,1
0.038392996228437,0,2,2,2,2,2,2
0.0060411077026529,0,3,3,3,3,3,3
5.9812540024784e-05,0,4,4,4,4,4,4
5.9812540024784e-05,0,5,5,5,5,5,5
5.285967493225e-29,0,0,1,1,1,1,1
4.830441079516e-30,0,0,2,2,2,2,2
2.3537404069876e-31,0,0,3,3,3,3,3
1.2851971453103e-31,0,0,4,4,4,4,4
9.7243393783398e-32,0,0,5,5,5,5,5
2.8036255956726e-31,0,1,2,2,2,2,2
5.6458324345948e-32,0,1,3,3,3,3,3
5.201235192063e-32,0,1,4,4,4,4,4
3.8229032758747e-32,0,1,5,5,5,5,5
3.6702787303277e-33,0,2,3,3,3,3,3
6.8822775950545e-33,0,2,4,4,4,4,4
5.0863886742273e-33,0,2,5,5,5,5,5
9.4052217449154e-34,0,3,4,4,4,4,4
8.2525733364501e-34,0,3,5,5,5,5,5
1.1437129538783e-35,0,4,5,5,5,5,5
8.3110407141877e-33,0,0,1,2,2,2,2
4.3564024206612e-35,0,0,1,3,3,3,3
2.2616474877005e-35,0,0,1,4,4,4,4
0,0,0,1,5,5,5,5
6.0559817026029e-37,0,0,2,3,3,3,3
4.9864238916151e-35,0,0,2,4,4,4,4
1.2773220117863e-35,0,0,2,5,5,5,5
2.2616474877005e-35,0,0,3,4,4,4,4
2.2462790842028e-36,0,0,3,5,5,5,5
3.6186359803208e-36,0,0,4,5,5,5,5
8.4742207610772e-36,0,1,2,3,3,3,3
4.9864238916151e-35,0,1,2,4,4,4,4
6.5128801849667e-37,0,1,2,5,5,5,5
6.0559817026029e-37,0,1,3,4,4,4,4
4.7849731971184e-37,0,1,3,5,5,5,5
1.1995661973331e-36,0,1,4,5,5,5,5
1.137261858829e-36,0,2,3,4,4,4,4
1.3291592214218e-38,0,2,3,5,5,5,5
5.615697710507e-37,0,2,4,5,5,5,5
2.0768112834715e-36,0,3,4,5,5,5,5
0,0,0,1,2,3,3,3
0,0,0,1,2,4,4,4
0,0,0,1,2,5,5,5
0,0,0,1,3,4,4,4
0,0,0,1,3,5,5,5
0,0,0,1,4,5,5,5
0,0,0,2,3,4,4,4
0,0,0,2,3,5,5,5
0,0,0,2,4,5,5,5
0,0,0,3,4,5,5,5
0,0,1,2,3,4,4,4
0,0,1,2,3,5,5,5
0,0,1,2,4,5,5,5
0,0,1,3,4,5,5,5
0,0,2,3,4,5,5,5
0,0,0,1,2,3,4,4
0,0,0,1,2,3,5,5
0,0,0,1,2,4,5,5
0,0,0,1,3,4,5,5
0,0,0,2,3,4,5,5
0,0,1,2,3,4,5,5
0,0,0,1,2,3,4,5

(modules/stochastic_tools/examples/surrogates/poly_chaos_normal.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 = MonteCarlo
    num_rows = 100000
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = initial
  []
[]

[Surrogates]
  [poly_chaos_avg]
    type = PolynomialChaos
    filename = 'poly_chaos_training_poly_chaos_avg.rd'
  []
  [poly_chaos_max]
    type = PolynomialChaos
    filename = 'poly_chaos_training_poly_chaos_max.rd'
  []
[]

[Reporters]
  [samp_avg]
    type = EvaluateSurrogate
    model = poly_chaos_avg
    sampler = sample
    parallel_type = ROOT
  []
  [samp_max]
    type = EvaluateSurrogate
    model = poly_chaos_max
    sampler = sample
    parallel_type = ROOT
  []
[]

# Computing statistics
[VectorPostprocessors]
  [stats_avg]
    type = PolynomialChaosStatistics
    pc_name = 'poly_chaos_avg'
    compute = 'mean stddev'
  []
  [stats_max]
    type = PolynomialChaosStatistics
    pc_name = 'poly_chaos_max'
    compute = 'mean stddev'
  []
  [sense_avg]
    type = PolynomialChaosLocalSensitivity
    pc_name = 'poly_chaos_avg'
    local_points = '5 10000 0.03 300'
  []
  [sense_max]
    type = PolynomialChaosLocalSensitivity
    pc_name = 'poly_chaos_max'
    local_points = '5 10000 0.03 300'
  []
  [sobol_avg]
    type = PolynomialChaosSobolStatistics
    pc_name = 'poly_chaos_avg'
    sensitivity_order = 'first second'
  []
  [sobol_max]
    type = PolynomialChaosSobolStatistics
    pc_name = 'poly_chaos_max'
    sensitivity_order = 'first second'
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/examples/surrogates/poly_chaos_uniform.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 = MonteCarlo
    num_rows = 100000
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = initial
  []
[]

[Surrogates]
  [poly_chaos_avg]
    type = PolynomialChaos
    filename = 'poly_chaos_training_poly_chaos_avg.rd'
  []
  [poly_chaos_max]
    type = PolynomialChaos
    filename = 'poly_chaos_training_poly_chaos_max.rd'
  []
[]

[Reporters]
  [samp_avg]
    type = EvaluateSurrogate
    model = poly_chaos_avg
    sampler = sample
    parallel_type = ROOT
  []
  [samp_max]
    type = EvaluateSurrogate
    model = poly_chaos_max
    sampler = sample
    parallel_type = ROOT
  []
[]

# Computing statistics
[VectorPostprocessors]
  [stats_avg]
    type = PolynomialChaosStatistics
    pc_name = 'poly_chaos_avg'
    compute = 'mean stddev'
  []
  [stats_max]
    type = PolynomialChaosStatistics
    pc_name = 'poly_chaos_max'
    compute = 'mean stddev'
  []
  [sense_avg]
    type = PolynomialChaosLocalSensitivity
    pc_name = 'poly_chaos_avg'
    local_points = '5 10000 0.03 300'
  []
  [sense_max]
    type = PolynomialChaosLocalSensitivity
    pc_name = 'poly_chaos_max'
    local_points = '5 10000 0.03 300'
  []
  [sobol_avg]
    type = PolynomialChaosSobolStatistics
    pc_name = 'poly_chaos_avg'
    sensitivity_order = 'first second'
  []
  [sobol_max]
    type = PolynomialChaosSobolStatistics
    pc_name = 'poly_chaos_max'
    sensitivity_order = 'first second'
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/test/tests/surrogates/poly_chaos/sobol.i)

[StochasticTools]
[]

[Distributions/uniform]
  type = Uniform
  lower_bound = 0
  upper_bound = 1
[]

[Samplers/sample]
  type = Quadrature
  order = 4
  distributions = 'uniform uniform uniform uniform uniform uniform'
  execute_on = 'initial'
[]

[VectorPostprocessors]
  [results]
    type = GFunction
    sampler = sample
    q_vector = '0 0.5 3 9 99 99'
    execute_on = INITIAL
    outputs = none
  []
  [sobol]
    type = PolynomialChaosSobolStatistics
    pc_name = poly_chaos
    sensitivity_order = 'all total'
    execute_on = timestep_end
  []
[]

[Surrogates]
  [poly_chaos]
    type = PolynomialChaos
    trainer = poly_chaos
  []
[]

[Trainers]
  [poly_chaos]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 4
    distributions = 'uniform uniform uniform uniform uniform uniform'
    sampler = sample
    response = results/g_values
  []
[]

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

(modules/combined/examples/stochastic/poly_chaos_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 = MonteCarlo
    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
  []
[]

[Surrogates]
  [temp_center_inner]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_temp_center_inner.rd'
  []
  [temp_center_outer]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_temp_center_outer.rd'
  []
  [temp_end_inner]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_temp_end_inner.rd'
  []
  [temp_end_outer]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_temp_end_outer.rd'
  []
  [dispx_center_inner]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispx_center_inner.rd'
  []
  [dispx_center_outer]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispx_center_outer.rd'
  []
  [dispx_end_inner]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispx_end_inner.rd'
  []
  [dispx_end_outer]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispx_end_outer.rd'
  []
  [dispz_inner]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispz_inner.rd'
  []
  [dispz_outer]
    type = PolynomialChaos
    filename = 'poly_chaos_train_uniform_out_dispz_outer.rd'
  []
[]

[VectorPostprocessors]
  [stats]
    type = PolynomialChaosStatistics
    pc_name = 'temp_center_inner  temp_center_outer  temp_end_inner  temp_end_outer
               dispx_center_inner dispx_center_outer dispx_end_inner dispx_end_outer
               dispz_inner dispz_outer'
    compute = 'mean stddev'
  []
  [sobol]
    type = PolynomialChaosSobolStatistics
    pc_name = 'temp_center_inner  temp_center_outer  temp_end_inner  temp_end_outer
               dispx_center_inner dispx_center_outer dispx_end_inner dispx_end_outer
               dispz_inner dispz_outer'
    sensitivity_order = 'first second total'
  []
[]

[Reporters]
  [storage]
    type = EvaluateSurrogate
    sampler = sample
    model = 'temp_center_inner  temp_center_outer  temp_end_inner  temp_end_outer
             dispx_center_inner dispx_center_outer dispx_end_inner dispx_end_outer
             dispz_inner dispz_outer'
    parallel_type = ROOT
  []
[]

[Outputs]
  csv = true
  execute_on = TIMESTEP_END
[]

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