SobolReporter

Compute SOBOL statistics values of a given VectorPostprocessor or Reporter objects and vectors.

Overview

This object computes the Sobol sensitivity indices following the procedure defined by Saltelli (2002). This includes the first-order and total-effect indices and optionally the second-order indices as well. The SobolReporter object only operates on result data generated from Sobol-based sampling strategy, which is provided by the Sobol.

Example Input File Syntax

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

g(x1,x2,,xn)=i=1n4xi2+qi1+qi,g(x_1, x_2, \ldots, x_n) = \prod_{i=1}^n\frac{|4x_i-2|+q_i}{1+q_i},

where q\vec{q} is defined in the input file, xx is the vector of model data, and nn is the number of input variables. The xx data is generated by the Sobol sampler object.

Sobol Statistics on VectorPostprocessor Data

The following shows the computation of sobol indices on data generated from a VectorPostprocessor. With the JSON output object, the resulting computation is outputted to a JSON file.

[Samplers]
  [sample]
    type = MonteCarlo
    distributions = 'uniform uniform uniform uniform uniform uniform'
    num_rows = 1024
    seed = 0
  []
  [resample]
    type = MonteCarlo
    distributions = 'uniform uniform uniform uniform uniform uniform'
    num_rows = 1024
    seed = 1
  []
  [sobol]
    type = Sobol
    sampler_a = sample
    sampler_b = resample
  []
[]

[VectorPostprocessors]
  [results]
    type = GFunction
    sampler = sobol
    q_vector = '0 0.5 3 9 99 99'
    execute_on = INITIAL
    outputs = none
    parallel_type = DISTRIBUTED
  []
[]

[Reporters]
  [sobol]
    type = SobolReporter
    sampler = sobol
    vectorpostprocessors = results
    ci_levels = '0.025 0.05 0.1 0.16 0.5 0.84 0.9 0.95 0.975'
    ci_replicates = 1000
    execute_on = FINAL
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]
(contrib/moose/modules/stochastic_tools/test/tests/reporters/sobol/sobol.i)

The resulting JSON output includes general information about the data, including how many parameters were observed and the indices being computed. This example includes FIRST_ORDER, SECOND_ORDER, and TOTAL indices. Following the reporter information, the values are shown as a pair of each set of indices and the associated confidence intervals (if requested). FIRST_ORDER and TOTAL indices are vectors with each element corresponding to a parameter. The SECOND_ORDER indices are represented by a matrix, where the row and column correspond to the parameter correlations.

{
    "reporters": {
        "sobol": {
            "confidence_intervals": {
                "levels": [
                    0.025,
                    0.05,
                    0.1,
                    0.16,
                    0.5,
                    0.84,
                    0.9,
                    0.95,
                    0.975
                ],
                "method": "percentile",
                "replicates": 1000,
                "seed": 1
            },
            "indices": [
                "FIRST_ORDER",
                "TOTAL",
                "SECOND_ORDER"
            ],
            "num_params": 6,
            "type": "SobolReporter",
            "values": {
                "results_g_values": {
                    "type": "SobolIndices<double>"
                }
            }
        }
    },
    "time_steps": [
        {
            "sobol": {
                "results_g_values": {
                    "FIRST_ORDER": [
                        [
                            0.5866463730226092,
                            0.23774753131409593,
                            0.034628969368923096,
                            0.00588135535195753,
                            5.433833280410634e-05,
                            5.85844315420159e-05
                        ],
                        [
                            [
                                0.48873441322758937,
                                0.19597876649065707,
                                0.028250202382804193,
                                0.004726384085063465,
                                4.3624927540252085e-05,
                                4.574103703227671e-05
                            ],
                            [
                                0.5038001816768876,
                                0.2008239248927682,
                                0.029210385453488835,
                                0.004908955867144933,
                                4.51049098372692e-05,
                                4.8299448856735816e-05
                            ],
                            [
                                0.5218411402520838,
                                0.20889879502232878,
                                0.030176567973180527,
                                0.0051120853453221135,
                                4.68786580325204e-05,
                                5.0721184085628405e-05
                            ],
                            [
                                0.5363136615738683,
                                0.2149758079596275,
                                0.031088125706042566,
                                0.005273002962177938,
                                4.817986124785616e-05,
                                5.2036183150586874e-05
                            ],
                            [
                                0.5852451598215687,
                                0.23829950323272125,
                                0.03445346548910488,
                                0.005886319761962729,
                                5.4105674337839574e-05,
                                5.821098841958302e-05
                            ],
                            [
                                0.6390425700173146,
                                0.2633215716159948,
                                0.03855547496475827,
                                0.006592766436013717,
                                6.061235990817635e-05,
                                6.54874781969199e-05
                            ],
                            [
                                0.657415074933954,
                                0.2722926564865208,
                                0.03965881501390822,
                                0.006834698757926061,
                                6.266436011124438e-05,
                                6.813169216207019e-05
                            ],
                            [
                                0.6867711618810028,
                                0.28424576782373434,
                                0.041521775869003893,
                                0.007190189741611754,
                                6.555657398023332e-05,
                                7.06401722981671e-05
                            ],
                            [
                                0.7048543291039749,
                                0.29489025166864885,
                                0.04342898237127246,
                                0.0074702308327570435,
                                6.815225504033798e-05,
                                7.30603410005782e-05
                            ]
                        ]
                    ],
                    "SECOND_ORDER": [
                        [
                            [
                                0.5866463730226092,
                                0.0963628746099523,
                                -0.013170497482959509,
                                0.004107328455384418,
                                -0.002343533765846617,
                                -0.0031280335291308248
                            ],
                            [
                                0.0963628746099523,
                                0.23774753131409593,
                                0.0009898353423217487,
                                -0.002219591284640554,
                                0.0009957820904085979,
                                0.0012075654305289396
                            ],
                            [
                                -0.013170497482959509,
                                0.0009898353423217487,
                                0.034628969368923096,
                                -0.0013454054622245096,
                                0.0028748550177293553,
                                0.003108228072270125
                            ],
                            [
                                0.004107328455384418,
                                -0.002219591284640554,
                                -0.0013454054622245096,
                                0.00588135535195753,
                                0.00011461865781733482,
                                8.019619965417626e-05
                            ],
                            [
                                -0.002343533765846617,
                                0.0009957820904085979,
                                0.0028748550177293553,
                                0.00011461865781733482,
                                5.433833280410634e-05,
                                7.909394757389275e-10
                            ],
                            [
                                -0.0031280335291308248,
                                0.0012075654305289396,
                                0.003108228072270125,
                                8.019619965417626e-05,
                                7.909394757389275e-10,
                                5.85844315420159e-05
                            ]
                        ],
                        [
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                                [
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                                    -0.12369720286178898,
                                    -0.1768237104073036,
                                    -0.1582025455828383,
                                    -0.15893885151421694,
                                    -0.15980225786369773
                                ],
                                [
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                                    0.19597876649065707,
                                    -0.060189713146096446,
                                    -0.05549033732394085,
                                    -0.05057100627716618,
                                    -0.05004379685766333
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                                    -0.060189713146096446,
                                    0.028250202382804193,
                                    -0.006940047277409975,
                                    -0.0010559702340158655,
                                    -0.0007910499543901384
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                                    -9.85900594370385e-06
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                                    4.574103703227671e-05
                                ]
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                                    -0.04738805822099376,
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                                ],
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                                    -0.04857801306851728,
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                                    -0.005761434664140225,
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                                    -0.00020953732842333983
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                                    -0.0004311475979742324,
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                                    4.51049098372692e-05,
                                    -8.21768616932424e-06
                                ],
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                                    4.8299448856735816e-05
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                                    0.23829950323272125,
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                                    -0.0019344231575314508,
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                                    0.03445346548910488,
                                    -0.0012750341613026565,
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                                    7.690438126196301e-05
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                                    0.0021395200965543815,
                                    0.001495473370274808,
                                    0.003004964722920344,
                                    0.00011227149653808294,
                                    5.4105674337839574e-05,
                                    -1.3446418042416892e-07
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                                [
                                    0.0018645655748735779,
                                    0.0018798947650462972,
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                                    7.690438126196301e-05,
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                                    0.00024165247646224658
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                                [
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                                    4.722953245157207e-06
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                                [
                                    0.07945936820212585,
                                    0.02735096086213068,
                                    0.0052983072379161195,
                                    0.00024165247646224658,
                                    4.722953245157207e-06,
                                    6.54874781969199e-05
                                ]
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                                    0.24636604760908265,
                                    0.0979089100931112,
                                    0.11064071325771418,
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                                    0.039237093861247685,
                                    0.03209574203829732,
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                                [
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                                    0.03209574203829732,
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                                [
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                                    0.005917221016011276,
                                    0.00029197814174826333,
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                                [
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                                    0.05313911292352466,
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                                [
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                                    0.00034695444193250276
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                                [
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                                    0.04756932678997322,
                                    0.006429632062906032,
                                    0.0003844269626809421,
                                    6.555657398023332e-05,
                                    7.582598156519483e-06
                                ],
                                [
                                    0.13174142186525617,
                                    0.047571396523455656,
                                    0.006778175593169511,
                                    0.00034695444193250276,
                                    7.582598156519483e-06,
                                    7.06401722981671e-05
                                ]
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                            [
                                [
                                    0.7048543291039749,
                                    0.3237433069760546,
                                    0.1570248521132983,
                                    0.1729344110192399,
                                    0.16258792026991475,
                                    0.16210202533274687
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                                [
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                                    0.29489025166864885,
                                    0.06467963081089789,
                                    0.055131314032976,
                                    0.058422307944948126,
                                    0.058863845952317195
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                                [
                                    0.1570248521132983,
                                    0.06467963081089789,
                                    0.04342898237127246,
                                    0.003823169675113633,
                                    0.00707821071628964,
                                    0.007324638546612534
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                                [
                                    0.1729344110192399,
                                    0.055131314032976,
                                    0.003823169675113633,
                                    0.0074702308327570435,
                                    0.00044580492658715786,
                                    0.0003917477706700586
                                ],
                                [
                                    0.16258792026991475,
                                    0.058422307944948126,
                                    0.00707821071628964,
                                    0.00044580492658715786,
                                    6.815225504033798e-05,
                                    9.253412388456094e-06
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                                [
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                                    0.058863845952317195,
                                    0.007324638546612534,
                                    0.0003917477706700586,
                                    9.253412388456094e-06,
                                    7.30603410005782e-05
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                        ]
                    ],
                    "TOTAL": [
                        [
                            0.7071753540241678,
                            0.3465927764290546,
                            0.09955612789901536,
                            0.020763701561386294,
                            0.007711012271259365,
                            0.00832407284710257
                        ],
                        [
                            [
                                0.6356652091140278,
                                0.21258503269518458,
                                -0.07116190437250247,
                                -0.16107696756820467,
                                -0.1798026749464532,
                                -0.1803098058843613
                            ],
                            [
                                0.6514358887786567,
                                0.23481461514625246,
                                -0.04119216231271938,
                                -0.1296990691025186,
                                -0.14682876851848214,
                                -0.14637308239284907
                            ],
                            [
                                0.6644429161273872,
                                0.264638586250981,
                                -0.009825886668100248,
                                -0.09752009826901031,
                                -0.1120156827916956,
                                -0.11163086869550298
                            ],
                            [
                                0.6748674046432122,
                                0.28163908390639325,
                                0.01673501996447746,
                                -0.06400955170577105,
                                -0.08017761388079059,
                                -0.08032374417583266
                            ],
                            [
                                0.7051305295837864,
                                0.3444144431952242,
                                0.0959426285569045,
                                0.01740682248537362,
                                0.004919266875244244,
                                0.0057751715418641325
                            ],
                            [
                                0.733612487841086,
                                0.39938696589761935,
                                0.16606229410417073,
                                0.09207083409320671,
                                0.07744942876341854,
                                0.07802152735069268
                            ],
                            [
                                0.7407292504926402,
                                0.413871814438142,
                                0.18445230677828328,
                                0.11375583333303119,
                                0.09753337205921075,
                                0.09868576418889008
                            ],
                            [
                                0.749589519371532,
                                0.4308275619230486,
                                0.20566789941995356,
                                0.13310461734327184,
                                0.11896974884671041,
                                0.12035990693841203
                            ],
                            [
                                0.7564935749281287,
                                0.4442641724892281,
                                0.22181722848018492,
                                0.14875377941003798,
                                0.13607316496336264,
                                0.13752509402477142
                            ]
                        ]
                    ]
                }
            },
            "time": 2.0,
            "time_step": 2
        }
    ]
}
(contrib/moose/modules/stochastic_tools/test/tests/reporters/sobol/gold/sobol_out.json)

Sobol Statistics on Reporter Data

Along with VectorPostprocessor data, the SobolReporter can compute indices on reporter data, which includes vector-type quantities of interest. Below shows the syntax required for reporter data.

[Reporters]
  [storage]
    type = StochasticReporter
    outputs = NONE
  []
  [sobol]
    type = SobolReporter
    reporters = 'storage/data:const:gf storage/data:const:gfa storage/data:const:gf_vec'
    ci_levels = '0.1 0.9'
    ci_replicates = 1000
    execute_on = FINAL
  []
[]
(contrib/moose/modules/stochastic_tools/test/tests/reporters/sobol/sobol_main.i)

Input Parameters

  • ci_levelsA vector of confidence levels to consider, values must be in (0, 1).

    C++ Type:std::vector<double>

    Unit:(no unit assumed)

    Controllable:No

    Description:A vector of confidence levels to consider, values must be in (0, 1).

  • ci_replicates10000The number of replicates to use when computing confidence level intervals.

    Default:10000

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The number of replicates to use when computing confidence level intervals.

  • ci_seed1The random number generator seed used for creating replicates while computing confidence level intervals.

    Default:1

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The random number generator seed used for creating replicates while computing confidence level intervals.

  • execute_onTIMESTEP_ENDThe 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:TIMESTEP_END

    C++ Type:ExecFlagEnum

    Unit:(no unit assumed)

    Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM

    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.

  • 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

    Unit:(no unit assumed)

    Controllable:No

    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.

  • reportersList of Reporter values to utilized for statistic computations.

    C++ Type:std::vector<ReporterName>

    Unit:(no unit assumed)

    Controllable:No

    Description:List of Reporter values to utilized for statistic computations.

  • samplerSobolSampler object.

    C++ Type:SamplerName

    Unit:(no unit assumed)

    Controllable:No

    Description:SobolSampler object.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

  • vectorpostprocessorsList of VectorPostprocessor(s) to utilized for statistic computations.

    C++ Type:std::vector<VectorPostprocessorName>

    Unit:(no unit assumed)

    Controllable:No

    Description:List of VectorPostprocessor(s) to utilized for statistic computations.

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

    Unit:(no unit assumed)

    Controllable:No

    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>

    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:Yes

    Description:Set the enabled status of the MooseObject.

  • execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

    Default:0

    C++ Type:int

    Unit:(no unit assumed)

    Controllable:No

    Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

  • force_postauxFalseForces the UserObject to be executed in POSTAUX

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in POSTAUX

  • force_preauxFalseForces the UserObject to be executed in PREAUX

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in PREIC during initial setup

  • outputsVector of output names where you would like to restrict the output of variables(s) associated with this object

    C++ Type:std::vector<OutputName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of output names where 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

    Unit:(no unit assumed)

    Controllable:No

    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

References

  1. Andrea Saltelli. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2):280–297, 2002. URL: https://doi.org/10.1016/S0010-4655(02)00280-1.[BibTeX]