NearestReporterCoordinatesFunction

This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point. All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.

Overview

This function computes values based on coordinate and time data. This data comes in the form of vector reporter or vectorpostprocessor values. The required parameter "value_name" is the name of the vector containing the values used to set the variable to. "x_coord_name"/"y_coord_name"/"z_coord_name" are vectors with the x-/y-/z-coordinate data. The auxkernel will set the variable's nodal/elemental values based on the nearest point in this data. "time_name" is the name of the time data; the kernel will linearly interpolate between two closest times for a certain coordinate, without extrapolating. "x_coord_name", "y_coord_name", "z_coord_name", and "time_name" will assume to be 0 when not specified. When specified, "x_coord_name", "y_coord_name", "z_coord_name", and "time_name" must all be the same length as "value_name".

Example Input File Syntax

Here are several examples of different combinations where x, y, z, and time data is specified:

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  active<<<{"description": "If specified only the blocks named will be visited and made active"}>>> = 'xyzt'
  [xx]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values1D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values1D/value'
  []
  [xy]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values2D/coordx'
    y_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s."}>>> = 'values2D/coordy'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values2D/value'
  []
  [xyz]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values3D/coordx'
    y_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s."}>>> = 'values3D/coordy'
    z_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing z-coordinate of points, default is assumed to be all 0s."}>>> = 'values3D/coordz'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values3D/value'
  []
  [xyzt]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    y_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordy'
    z_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing z-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordz'
    time_name<<<{"description": "Name of vector-postprocessor or reporter vector containing time, default is assumed to be all 0s."}>>> = 'values4D/time'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values4D/value'
  []

  [errorv]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values1D/val'
  []
  [errorx]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values1D/coordx'
    y_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values4D/value'
  []
  [errory]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    y_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s."}>>> = 'values1D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values4D/value'
  []
  [errorz]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    variable = val
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    z_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing z-coordinate of points, default is assumed to be all 0s."}>>> = 'values1D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values4D/value'
  []
  [errort]
    type = NearestReporterCoordinatesFunction<<<{"description": "This Function finds the nearest point in the specified vectors of coordinates and returns the values specified in the vector of values at the index of the nearest point.  All the vectors must be specified using either vector postprocessors or reporter vectors. This function interpolates linearly in time with transient data.", "href": "NearestReporterCoordinatesFunction.html"}>>>
    x_coord_name<<<{"description": "Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s."}>>> = 'values4D/coordx'
    time_name<<<{"description": "Name of vector-postprocessor or reporter vector containing time, default is assumed to be all 0s."}>>> = 'values1D/coordx'
    value_name<<<{"description": "Name of vector-postprocessor or reporter vector containing value data."}>>> = 'values4D/value'
  []
[]

[Reporters<<<{"href": "../../syntax/Reporters/index.html"}>>>]
  [values1D]
    type = ConstantReporter<<<{"description": "Reporter with constant values to be accessed by other objects, can be modified using transfers.", "href": "../reporters/ConstantReporter.html"}>>>
    real_vector_names<<<{"description": "Names for each vector of reals value."}>>> = 'coordx value'
    real_vector_values<<<{"description": "Values for vectors of reals."}>>> = '0.25 0.75;
                          0.00 1.00'
  []
  [values2D]
    type = ConstantReporter<<<{"description": "Reporter with constant values to be accessed by other objects, can be modified using transfers.", "href": "../reporters/ConstantReporter.html"}>>>
    real_vector_names<<<{"description": "Names for each vector of reals value."}>>> = 'coordx coordy value'
    real_vector_values<<<{"description": "Values for vectors of reals."}>>> = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          0.00 1.00 2.00 3.00'
  []
  [values3D]
    type = ConstantReporter<<<{"description": "Reporter with constant values to be accessed by other objects, can be modified using transfers.", "href": "../reporters/ConstantReporter.html"}>>>
    real_vector_names<<<{"description": "Names for each vector of reals value."}>>> = 'coordx coordy coordz value'
    real_vector_values<<<{"description": "Values for vectors of reals."}>>> = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;
                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00'
  []
  [values4D]
    type = ConstantReporter<<<{"description": "Reporter with constant values to be accessed by other objects, can be modified using transfers.", "href": "../reporters/ConstantReporter.html"}>>>
    real_vector_names<<<{"description": "Names for each vector of reals value."}>>> = 'coordx coordy coordz time value'
    real_vector_values<<<{"description": "Values for vectors of reals."}>>> = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;

                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;

                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;

                          0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
                          0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
                          1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00;

                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
                          8.00 9.00 10.0 11.0 12.0 13.0 14.0 15.0
                          16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0'
  []
[]

Run this test to see how the function interpolates the data between specified times.

Input Parameters

value_nameName of vector-postprocessor or reporter vector containing value data.
C++ Type:ReporterName
Controllable:No
Description:Name of vector-postprocessor or reporter vector containing value data.

Required Parameters

time_nameName of vector-postprocessor or reporter vector containing time, default is assumed to be all 0s.
C++ Type:ReporterName
Controllable:No
Description:Name of vector-postprocessor or reporter vector containing time, default is assumed to be all 0s.
x_coord_nameName of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s.
C++ Type:ReporterName
Controllable:No
Description:Name of vector-postprocessor or reporter vector containing x-coordinate of points, default is assumed to be all 0s.
y_coord_nameName of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s.
C++ Type:ReporterName
Controllable:No
Description:Name of vector-postprocessor or reporter vector containing y-coordinate of points, default is assumed to be all 0s.
z_coord_nameName of vector-postprocessor or reporter vector containing z-coordinate of points, default is assumed to be all 0s.
C++ Type:ReporterName
Controllable:No
Description:Name of vector-postprocessor or reporter vector containing z-coordinate of points, default is assumed to be all 0s.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/optimization/test/tests/optimizationreporter/bimaterial/grad.i)
(modules/optimization/examples/simpleTransient/nonlinear_forward_and_adjoint.i)
(modules/optimization/examples/materialFrequency/wave1D/model_grad.i)
(modules/combined/test/tests/optimization/invOpt_elasticity_modular/grad.i)
(modules/optimization/examples/materialTransient/forward_and_adjoint.i)
(modules/optimization/test/tests/functions/nearest_reporter_coord/nearest_reporter_point.i)
(modules/optimization/test/tests/optimizationreporter/bimaterial/model.i)
(modules/optimization/examples/simpleTransient/forward_and_adjoint.i)
(modules/optimization/examples/simpleTransient/adjoint.i)
(modules/optimization/examples/materialTransient/forward.i)
(modules/optimization/test/tests/vectorpostprocessors/element_source_inner_product/element_source_inner_product.i)
(modules/combined/test/tests/optimization/invOpt_elasticity_modular/forward.i)
(modules/optimization/examples/materialTransient/gradient.i)
(modules/optimization/test/tests/optimizationreporter/bimaterial/model_and_adjoint.i)
(modules/optimization/examples/simpleTransient/forward.i)

(modules/optimization/test/tests/functions/nearest_reporter_coord/nearest_reporter_point.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
  []
[]

[AuxVariables]
  [val]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [val_aux]
    type = FunctionAux
    variable = val
    function = 'xyzt'
    execute_on = 'initial timestep_end'
  []
[]

[Functions]
  active = 'xyzt'
  [xx]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values1D/coordx'
    value_name = 'values1D/value'
  []
  [xy]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values2D/coordx'
    y_coord_name = 'values2D/coordy'
    value_name = 'values2D/value'
  []
  [xyz]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values3D/coordx'
    y_coord_name = 'values3D/coordy'
    z_coord_name = 'values3D/coordz'
    value_name = 'values3D/value'
  []
  [xyzt]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    y_coord_name = 'values4D/coordy'
    z_coord_name = 'values4D/coordz'
    time_name = 'values4D/time'
    value_name = 'values4D/value'
  []

  [errorv]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    value_name = 'values1D/val'
  []
  [errorx]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values1D/coordx'
    y_coord_name = 'values4D/coordx'
    value_name = 'values4D/value'
  []
  [errory]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    y_coord_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
  [errorz]
    type = NearestReporterCoordinatesFunction
    variable = val
    x_coord_name = 'values4D/coordx'
    z_coord_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
  [errort]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    time_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
[]

[Reporters]
  [values1D]
    type = ConstantReporter
    real_vector_names = 'coordx value'
    real_vector_values = '0.25 0.75;
                          0.00 1.00'
  []
  [values2D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy value'
    real_vector_values = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          0.00 1.00 2.00 3.00'
  []
  [values3D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy coordz value'
    real_vector_values = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;
                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00'
  []
  [values4D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy coordz time value'
    real_vector_values = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;

                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;

                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;

                          0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
                          0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
                          1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00;

                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
                          8.00 9.00 10.0 11.0 12.0 13.0 14.0 15.0
                          16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0'
  []
[]

[Problem]
  solve = false
  kernel_coverage_check = false
  skip_nl_system_check = true
[]

[Executioner]
  type = Transient
  dt = 0.1
  end_time = 1
[]

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/optimizationreporter/bimaterial/grad.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 16
    ny = 16
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
[]

[Variables]
  [adjoint_T]
  []
[]

[Kernels]
  [conduction]
    type = MatDiffusion
    diffusivity = diffusivity
    variable = adjoint_T
  []
[]

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [data]
    type = ConstantReporter
    real_vector_names = 'coordx coordy diffusivity'
    real_vector_values = '0 0; -2 2; 5 10'
  []
[]

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = adjoint_T
    x_coord_name = misfit/measurement_xcoord
    y_coord_name = misfit/measurement_ycoord
    z_coord_name = misfit/measurement_zcoord
    value_name = misfit/misfit_values
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = adjoint_T
    boundary = bottom
    value = 0
  []
[]

[AuxVariables]
  [temperature_forward]
  []
[]

[Functions]
  [diffusivity_function]
    type = NearestReporterCoordinatesFunction
    x_coord_name = data/coordx
    y_coord_name = data/coordy
    value_name = data/diffusivity
  []
[]

[Materials] #same material as what was used in the forward model
  [mat]
    type = GenericFunctionMaterial
    prop_names = diffusivity
    prop_values = diffusivity_function
  []
[]

[VectorPostprocessors]
  [gradvec]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = adjoint_T
    forward_variable = temperature_forward
    function = diffusivity_function
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

[Outputs]
  console = false
  file_base = 'adjoint'
[]

(modules/optimization/examples/simpleTransient/nonlinear_forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    xmax = 1
    ymin = -1
    ymax = 1
  []
[]

[Variables]
  [u]
  []
[]

[VectorPostprocessors]
  [src_values]
    type = CSVReader
    csv_file = source_params.csv
    header = true
    outputs = none
  []
[]

[ICs]
  [initial]
    type = FunctionIC
    variable = u
    function = exact
  []
[]

[Kernels]
  [dt]
    type = ADTimeDerivative
    variable = u
  []
  [diff]
    type = ADMatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = ADBodyForce
    variable = u
    function = source
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[Materials]
  [diffc]
    type = ADParsedMaterial
    property_name = D
    expression = '1 + u'
    coupled_variables = u
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = '2*exp(-2.0*(x - sin(2*pi*t))^2)*exp(-2.0*(y - cos(2*pi*t))^2)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/pi'
  []
  [source]
    type = NearestReporterCoordinatesFunction
    x_coord_name = src_values/coordx
    y_coord_name = src_values/coordy
    time_name = src_values/time
    value_name = src_values/values
  []
[]

[Preconditioning]
  [nl0]
    type = SMP
    nl_sys = 'nl0'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
  [adjoint]
    type = SMP
    nl_sys = 'adjoint'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = TransientAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint

  num_steps = 100
  end_time = 1

  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Reporters]
  [measured_data]
    type = OptimizationData
    measurement_file = mms_data.csv
    file_xcoord = x
    file_ycoord = y
    file_zcoord = z
    file_time = t
    file_value = u
    variable = u
    execute_on = timestep_end
    objective_name = objective_value
    outputs = none
  []
[]

[Postprocessors]
  [topRight_pp]
    type = PointValue
    point = '0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomRight_pp]
    type = PointValue
    point = '-0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomLeft_pp]
    type = PointValue
    point = '-0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [topLeft_pp]
    type = PointValue
    point = '0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  csv = true
  console = false
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
  kernel_coverage_check = false
[]

[Variables]
  [u_adjoint]
    solver_sys = adjoint
    outputs = none
  []
[]

[DiracKernels]
  [misfit]
    type = ReporterTimePointSource
    variable = u_adjoint
    value_name = measured_data/misfit_values
    x_coord_name = measured_data/measurement_xcoord
    y_coord_name = measured_data/measurement_ycoord
    z_coord_name = measured_data/measurement_zcoord
    time_name = measured_data/measurement_time
  []
[]

[VectorPostprocessors]
  [adjoint]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = u_adjoint
    function = source
    execute_on = ADJOINT_TIMESTEP_END
    outputs = none
  []
[]

(modules/optimization/examples/materialFrequency/wave1D/model_grad.i)

id = 1
frequencyHz = 1.0
omega = '${fparse 2*3.14159265359*frequencyHz}'

[Problem]
  nl_sys_names = 'nl0 adjoint'
  kernel_coverage_check = false
  skip_nl_system_check = true
[]

[Preconditioning]
  [nl0]
    type = SMP
    nl_sys = 'nl0'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
    full = true
  []
  [adjoint]
    type = SMP
    nl_sys = 'adjoint'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
    full = true
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

[Outputs]
  csv = false
  console = false
  json = false
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmax = 2
[]

[Variables]
  [ur]
  []
  [ui]
  []
  [uradj]
    initial_condition = 0
    solver_sys = adjoint
  []
  [uiadj]
    initial_condition = 0
    solver_sys = adjoint
  []
[]

[Kernels]
  [stiff]
    type = MatDiffusion
    variable = ur
    diffusivity = G
  []
  [mass]
    type = Reaction
    variable = ur
    rate = '${fparse -1.0*omega*omega}'
  []
  [stiffV]
    type = MatDiffusion
    variable = ui
    diffusivity = G
  []
  [massV]
    type = Reaction
    variable = ui
    rate = '${fparse -1.0*omega*omega}'
  []
[]

[BCs]
  [leftU]
    type = CoupledVarNeumannBC
    boundary = left
    variable = ur
    coef = 2.0
    v = ui
  []
  [leftV]
    type = CoupledVarNeumannBC
    boundary = left
    variable = ui
    coef = -2.0
    v = ur
  []
  [right]
    type = NeumannBC
    variable = ur
    boundary = right
    value = 1
  []
[]

[Materials]
  [G]
    type = GenericFunctionMaterial
    prop_names = G
    prop_values = G_function
  []
[]

[Functions]
  [G_function]
    type = NearestReporterCoordinatesFunction
    x_coord_name = parameters/coordx
    value_name = parameters/G
  []
[]

[Reporters]
  [parameters]
    type = ConstantReporter
    real_vector_names = 'coordx G'
    # 'True value when used to generate synthetic data'
    # real_vector_values = '5.0 15.0; 4.0 4.0'
    real_vector_values = '1.0; 4.0'
  []
[]

[DiracKernels]
  [misfit_ur]
    type = ReporterPointSource
    variable = uradj
    x_coord_name = measure_data_ur/measurement_xcoord
    y_coord_name = measure_data_ur/measurement_ycoord
    z_coord_name = measure_data_ur/measurement_zcoord
    value_name = measure_data_ur/misfit_values
  []
  [misfit_ui]
    type = ReporterPointSource
    variable = uiadj
    x_coord_name = measure_data_ui/measurement_xcoord
    y_coord_name = measure_data_ui/measurement_ycoord
    z_coord_name = measure_data_ui/measurement_zcoord
    value_name = measure_data_ui/misfit_values
  []
[]

[VectorPostprocessors]
  [gradient_from_real]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = uradj
    forward_variable = ur
    function = G_function
    execute_on = ADJOINT_TIMESTEP_END
    # Just to confirm this happens BEFORE the gradient calcutions
    execution_order_group = -1
  []
  [gradient_from_imag]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = uiadj
    forward_variable = ui
    function = G_function
    execute_on = ADJOINT_TIMESTEP_END
    # Just to confirm this happens BEFORE the gradient calcutions
    execution_order_group = -1
  []
[]

[Reporters]
  [measure_data_ur]
    type = OptimizationData
    objective_name = obj_val
    variable = 'ur'
    file_value = 'value'
    measurement_file = 'measurement/frequency_ur_${id}.csv'
  []
  [measure_data_ui]
    type = OptimizationData
    objective_name = obj_val
    variable = 'ui'
    file_value = 'value'
    measurement_file = 'measurement/frequency_ui_${id}.csv'
  []
  [gradient]
    type = ParsedVectorReporter
    name = gradient
    reporter_names = 'gradient_from_real/inner_product gradient_from_imag/inner_product'
    reporter_symbols = 'a b'
    expression = 'a+b'
    execute_on = ADJOINT_TIMESTEP_END
    execution_order_group = 0
  []
  [objective]
    type = ParsedScalarReporter
    name = objective
    reporter_names = 'measure_data_ur/obj_val measure_data_ui/obj_val'
    reporter_symbols = 'a b'
    expression = 'a+b'
    execute_on = ADJOINT_TIMESTEP_END
    # Just to confirm this happens after the gradient calcutions
    execution_order_group = 1
  []
[]

(modules/combined/test/tests/optimization/invOpt_elasticity_modular/grad.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 11
    ny = 11
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
  displacements = 'adj_disp_x adj_disp_y'
[]

[Variables]
  # adjoint
  [adj_disp_x]
  []
  [adj_disp_y]
  []
[]

[AuxVariables]
  [dummy]
  []
  [T]
  []
  # displacement variables to be transferred from the forward app
  # we use them to compute stress and stress derivative wrt E
  [disp_x]
  []
  [disp_y]
  []
[]

[DiracKernels]
  [misfit_is_adjoint_force]
    type = ReporterPointSource
    variable = adj_disp_x
    x_coord_name = misfit/measurement_xcoord
    y_coord_name = misfit/measurement_ycoord
    z_coord_name = misfit/measurement_zcoord
    value_name = misfit/misfit_values
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      displacements = 'adj_disp_x adj_disp_y'
      [adjoint]
        strain = SMALL
        new_system = true
        formulation = TOTAL
        incremental = true
        volumetric_locking_correction = false
        displacements = 'adj_disp_x adj_disp_y'
        # add base name to distinguish between forward and adjoint
        # the total lagrangian formulation does not add base_name correctly without setting both, which should be improved
        base_name = 'adjoint'
        strain_base_name = 'adjoint'
      []
    []
  []
[]

[NEML2]
  input = 'elasticity.i'
  verbose = true
  device = 'cpu'
  [forward]
    model = 'forward_elasticity_model'

    moose_input_types = 'MATERIAL'
    moose_inputs = 'forward_strain'
    neml2_inputs = 'forces/E'

    moose_parameter_types = 'MATERIAL'
    moose_parameters = 'E_material'
    neml2_parameters = 'E'

    moose_output_types = 'MATERIAL'
    moose_outputs = 'forward_stress'
    neml2_outputs = 'state/S'

    moose_parameter_derivative_types = 'MATERIAL'
    moose_parameter_derivatives = 'forward_dstress_dE'
    neml2_parameter_derivatives = 'state/S E'
  []
  [adjoint]
    model = 'adjoint_elasticity_model'

    moose_input_types = 'MATERIAL'
    moose_inputs = 'adjoint_strain'
    neml2_inputs = 'forces/E'

    moose_parameter_types = 'MATERIAL'
    moose_parameters = 'E_material'
    neml2_parameters = 'E'

    moose_output_types = 'MATERIAL'
    moose_outputs = 'adjoint_stress'
    neml2_outputs = 'state/S'

    moose_derivative_types = 'MATERIAL'
    moose_derivatives = 'adjoint_jacobian'
    neml2_derivatives = 'state/S forces/E'
  []
[]

[BCs]
  [bottom_ux]
    type = DirichletBC
    variable = adj_disp_x
    boundary = bottom
    value = 0.0
  []
  [bottom_uy]
    type = DirichletBC
    variable = adj_disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Materials]
  [E_material]
    type = GenericFunctionMaterial
    prop_names = 'E_material'
    prop_values = 'E'
  []

  # forward
  [forward_strain]
    type = ComputeLagrangianStrain
    displacements = 'disp_x disp_y'
    base_name = 'forward'
  []
  [convert_forward_strain]
    type = RankTwoTensorToSymmetricRankTwoTensor
    from = 'forward_mechanical_strain'
    to = 'forward_strain'
  []

  # adjoint
  [convert_adjoint_strain]
    type = RankTwoTensorToSymmetricRankTwoTensor
    from = 'adjoint_mechanical_strain'
    to = 'adjoint_strain'
  []
  [adjoint_stress]
    type = ComputeLagrangianObjectiveCustomSymmetricStress
    custom_small_stress = 'adjoint_stress'
    custom_small_jacobian = 'adjoint_jacobian'
    base_name = 'adjoint'
  []
[]

[Functions]
  [E]
    type = NearestReporterCoordinatesFunction
    x_coord_name = parametrization/coordx
    y_coord_name = parametrization/coordy
    value_name = parametrization/youngs_modulus
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = 'adj_disp_x'
  []
  [misfit]
    type = OptimizationData
  []
  [parametrization]
    type = ConstantReporter
    real_vector_names = 'coordx coordy youngs_modulus'
    real_vector_values = '0 0 0; ${fparse 8/3} 0 ${fparse -8/3}; 5 5 5'
  []
[]

[VectorPostprocessors]
  [grad_youngs_modulus]
    type = AdjointStrainSymmetricStressGradInnerProduct
    stress_derivative_name = 'forward_dstress_dE'
    adjoint_strain_name = 'adjoint_mechanical_strain'
    variable = dummy
    function = E
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  # we do not compute them together as this is overwritting DiracKernel's residual calculation, which should be improved
  residual_and_jacobian_together = false
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-14
[]

[Outputs]
  file_base = 'adjoint'
  console = false
[]

(modules/optimization/examples/materialTransient/forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 10
    ny = 10
  []
[]

[Variables/u]
  initial_condition = 0
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'right top'
    value = 0
  []
[]

[Materials]
  [diffc]
    type = GenericFunctionMaterial
    prop_names = 'D'
    prop_values = 'diffc_fun'
    output_properties = 'D'
    outputs = 'exodus'
  []
[]

[Functions]
  [diffc_fun]
    type = NearestReporterCoordinatesFunction
    value_name = 'diffc_rep/D_vals'
    x_coord_name = 'diffc_rep/D_x_coord'
    y_coord_name = 'diffc_rep/D_y_coord'
  []
[]

[Reporters]
  [diffc_rep]
    type = ConstantReporter
    real_vector_names = 'D_x_coord D_y_coord D_vals'
    real_vector_values = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          1  0.2   0.2   0.05' # Reference solution
    outputs = none
  []
  [data]
    type = OptimizationData
    objective_name = objective_value
    variable = u
    outputs = none
  []
[]

[Postprocessors]
  [D1]
    type = PointValue
    variable = D
    point = '0.25 0.25 0'
  []
  [D2]
    type = PointValue
    variable = D
    point = '0.75 0.25 0'
  []
  [D3]
    type = PointValue
    variable = D
    point = '0.25 0.75 0'
  []
  [D4]
    type = PointValue
    variable = D
    point = '0.75 0.75 0'
  []
[]

[Executioner]
  type = TransientAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12
  l_tol = 1e-12

  dt = 0.1
  num_steps = 10
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
  kernel_coverage_check = false
[]

[Variables]
  [u_adjoint]
    initial_condition = 0
    solver_sys = adjoint
    outputs = none
  []
[]

[DiracKernels]
  [misfit]
    type = ReporterTimePointSource
    variable = u_adjoint
    value_name = data/misfit_values
    x_coord_name = data/measurement_xcoord
    y_coord_name = data/measurement_ycoord
    z_coord_name = data/measurement_zcoord
    time_name = data/measurement_time
  []
[]

[VectorPostprocessors]
  [adjoint]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = u_adjoint
    forward_variable = u
    function = diffc_fun
    execute_on = ADJOINT_TIMESTEP_END
    outputs = none
  []
[]

[Outputs]
  # The default exodus object executes only during the forward system solve,
  # so the adjoint variable in the resulting file will show only 0.
  # Unfortunately, there is no way to output the adjoint variable with Exodus.
  exodus = true
  console = false
[]

(modules/optimization/test/tests/functions/nearest_reporter_coord/nearest_reporter_point.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
  []
[]

[AuxVariables]
  [val]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [val_aux]
    type = FunctionAux
    variable = val
    function = 'xyzt'
    execute_on = 'initial timestep_end'
  []
[]

[Functions]
  active = 'xyzt'
  [xx]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values1D/coordx'
    value_name = 'values1D/value'
  []
  [xy]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values2D/coordx'
    y_coord_name = 'values2D/coordy'
    value_name = 'values2D/value'
  []
  [xyz]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values3D/coordx'
    y_coord_name = 'values3D/coordy'
    z_coord_name = 'values3D/coordz'
    value_name = 'values3D/value'
  []
  [xyzt]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    y_coord_name = 'values4D/coordy'
    z_coord_name = 'values4D/coordz'
    time_name = 'values4D/time'
    value_name = 'values4D/value'
  []

  [errorv]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    value_name = 'values1D/val'
  []
  [errorx]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values1D/coordx'
    y_coord_name = 'values4D/coordx'
    value_name = 'values4D/value'
  []
  [errory]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    y_coord_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
  [errorz]
    type = NearestReporterCoordinatesFunction
    variable = val
    x_coord_name = 'values4D/coordx'
    z_coord_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
  [errort]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    time_name = 'values1D/coordx'
    value_name = 'values4D/value'
  []
[]

[Reporters]
  [values1D]
    type = ConstantReporter
    real_vector_names = 'coordx value'
    real_vector_values = '0.25 0.75;
                          0.00 1.00'
  []
  [values2D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy value'
    real_vector_values = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          0.00 1.00 2.00 3.00'
  []
  [values3D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy coordz value'
    real_vector_values = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;
                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00'
  []
  [values4D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy coordz time value'
    real_vector_values = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;

                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;

                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;

                          0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
                          0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
                          1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00;

                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
                          8.00 9.00 10.0 11.0 12.0 13.0 14.0 15.0
                          16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0'
  []
[]

[Problem]
  solve = false
  kernel_coverage_check = false
  skip_nl_system_check = true
[]

[Executioner]
  type = Transient
  dt = 0.1
  end_time = 1
[]

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/optimizationreporter/bimaterial/model.i)

# Steady state Heat conduction in a 2D domain with two diffusivities
# The domain is -4 <= x <= 4 and -4 <= y <= 4
# The top-half of the domain (y > 0) has high diffusivity
# The bottom-half of the domain (y < 0) has low diffusivity

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 16
    ny = 16
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = diffusivity
  []
  [heat_source]
    type = BodyForce
    value = 100
    variable = temperature
  []
[]

[AuxVariables]
  [grad_Tx]
    order = CONSTANT
    family = MONOMIAL
  []
  [grad_Ty]
    order = CONSTANT
    family = MONOMIAL
  []
  [grad_Tz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 0
  []
[]

[Functions]
  [diffusivity_function]
    type = NearestReporterCoordinatesFunction
    x_coord_name = data/coordx
    y_coord_name = data/coordy
    value_name = data/diffusivity
  []
[]

[Materials]
  [mat]
    type = GenericFunctionMaterial
    prop_names = diffusivity
    prop_values = diffusivity_function
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    objective_name = objective_value
  []
  [data]
    type = ConstantReporter
    real_vector_names = 'coordx coordy diffusivity'
    real_vector_values = '0 0; -2 2; 5 10'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

[Outputs]
  file_base = 'forward'
  console = false
[]

(modules/optimization/examples/simpleTransient/forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    xmax = 1
    ymin = -1
    ymax = 1
  []
[]

[Variables]
  [u]
  []
[]

[VectorPostprocessors]
  [src_values]
    type = CSVReader
    csv_file = source_params.csv
    header = true
    outputs = none
  []
[]

[ICs]
  [initial]
    type = FunctionIC
    variable = u
    function = exact
  []
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    function = source
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = '2*exp(-2.0*(x - sin(2*pi*t))^2)*exp(-2.0*(y - cos(2*pi*t))^2)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/pi'
  []
  [source]
    type = NearestReporterCoordinatesFunction
    x_coord_name = src_values/coordx
    y_coord_name = src_values/coordy
    time_name = src_values/time
    value_name = src_values/values
  []
[]

[Preconditioning]
  [nl0]
    type = SMP
    nl_sys = 'nl0'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
  [adjoint]
    type = SMP
    nl_sys = 'adjoint'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = TransientAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint

  num_steps = 100
  end_time = 1

  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Reporters]
  [measured_data]
    type = OptimizationData
    measurement_file = mms_data.csv
    file_xcoord = x
    file_ycoord = y
    file_zcoord = z
    file_time = t
    file_value = u
    variable = u
    execute_on = timestep_end
    objective_name = objective_value
    outputs = none
  []
[]

[Postprocessors]
  [topRight_pp]
    type = PointValue
    point = '0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomRight_pp]
    type = PointValue
    point = '-0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomLeft_pp]
    type = PointValue
    point = '-0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [topLeft_pp]
    type = PointValue
    point = '0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  csv = true
  console = false
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
  kernel_coverage_check = false
[]

[Variables]
  [u_adjoint]
    solver_sys = adjoint
    outputs = none
  []
[]

[DiracKernels]
  [misfit]
    type = ReporterTimePointSource
    variable = u_adjoint
    value_name = measured_data/misfit_values
    x_coord_name = measured_data/measurement_xcoord
    y_coord_name = measured_data/measurement_ycoord
    z_coord_name = measured_data/measurement_zcoord
    time_name = measured_data/measurement_time
  []
[]

[VectorPostprocessors]
  [adjoint]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = u_adjoint
    function = source
    execute_on = ADJOINT_TIMESTEP_END
    outputs = none
  []
[]

(modules/optimization/examples/simpleTransient/adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    xmax = 1
    ymin = -1
    ymax = 1
  []
[]

[Variables]
  [u]
  []
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[Reporters]
  [measured_data]
    type = OptimizationData
    measurement_file = mms_data.csv
    file_xcoord = x
    file_ycoord = y
    file_zcoord = z
    file_time = t
    file_value = u
  []
[]

[DiracKernels]
  [misfit]
    type = ReporterTimePointSource
    variable = u
    value_name = measured_data/misfit_values
    x_coord_name = measured_data/measurement_xcoord
    y_coord_name = measured_data/measurement_ycoord
    z_coord_name = measured_data/measurement_zcoord
    time_name = measured_data/measurement_time
    reverse_time_end = 1
  []
[]

[VectorPostprocessors]
  [src_values]
    type = CSVReader
    csv_file = source_params.csv
    header = true
  []
[]

[Functions]
  [source]
    type = NearestReporterCoordinatesFunction
    x_coord_name = src_values/coordx
    y_coord_name = src_values/coordy
    time_name = src_values/time
    value_name = src_values/values
  []
[]

[VectorPostprocessors]
  [adjoint]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = u
    function = source
    reverse_time_end = 1
  []
[]

[Executioner]
  type = Transient

  num_steps = 100
  end_time = 1

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  reuse_preconditioner=true
  reuse_preconditioner_max_linear_its=50
[]

[Outputs]
  console = false
[]

(modules/optimization/examples/materialTransient/forward.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 10
    ny = 10
  []
[]

[Variables/u]
  initial_condition = 0
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'right top'
    value = 0
  []
[]

[Materials]
  [diffc]
    type = GenericFunctionMaterial
    prop_names = 'D'
    prop_values = 'diffc_fun'
    output_properties = 'D'
    outputs = 'exodus'
  []
[]

[Functions]
  [diffc_fun]
    type = NearestReporterCoordinatesFunction
    value_name = 'diffc_rep/D_vals'
    x_coord_name = 'diffc_rep/D_x_coord'
    y_coord_name = 'diffc_rep/D_y_coord'
  []
[]

[Reporters]
  [diffc_rep]
    type = ConstantReporter
    real_vector_names = 'D_x_coord D_y_coord D_vals'
    real_vector_values = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          1  0.2   0.2   0.05' # Reference solution
    outputs = none
  []
  [data]
    type = OptimizationData
    variable = u
    measurement_points = '0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0
                          0.25 0.25 0  0.25 0.75 0  0.75 0.25 0  0.75 0.75 0'
    measurement_times = '0.1 0.1 0.1 0.1
                         0.2 0.2 0.2 0.2
                         0.3 0.3 0.3 0.3
                         0.4 0.4 0.4 0.4
                         0.5 0.5 0.5 0.5
                         0.6 0.6 0.6 0.6
                         0.7 0.7 0.7 0.7
                         0.8 0.8 0.8 0.8
                         0.9 0.9 0.9 0.9
                         1.0 1.0 1.0 1.0'
    measurement_values = '0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0
                          0 0 0 0'
    objective_name = objective_value
    outputs = none
  []
[]

[Postprocessors]
  [D1]
    type = PointValue
    variable = D
    point = '0.25 0.25 0'
  []
  [D2]
    type = PointValue
    variable = D
    point = '0.75 0.25 0'
  []
  [D3]
    type = PointValue
    variable = D
    point = '0.25 0.75 0'
  []
  [D4]
    type = PointValue
    variable = D
    point = '0.75 0.75 0'
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12

  dt = 0.1
  num_steps = 10
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/optimization/test/tests/vectorpostprocessors/element_source_inner_product/element_source_inner_product.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
  []
[]

[AuxVariables]
  [u]
    initial_condition = 1
  []
[]

[AuxKernels]
  [u_val]
    type = ParsedAux
    variable = u
    use_xyzt = true
    function = 't'
  []
[]

[Functions]
  [xyzt]
    type = NearestReporterCoordinatesFunction
    x_coord_name = 'values4D/coordx'
    y_coord_name = 'values4D/coordy'
    z_coord_name = 'values4D/coordz'
    time_name = 'values4D/time'
    value_name = 'values4D/value'
  []
[]

[Reporters]
  [values4D]
    type = ConstantReporter
    real_vector_names = 'coordx coordy coordz time value'
    real_vector_values = '0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75
                          0.25 0.75 0.25 0.75 0.25 0.75 0.25 0.75;

                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75
                          0.25 0.25 0.75 0.75 0.25 0.25 0.75 0.75;

                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75
                          0.25 0.25 0.25 0.25 0.75 0.75 0.75 0.75;

                          0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
                          0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
                          1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00;

                          0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
                          8.00 9.00 10.0 11.0 12.0 13.0 14.0 15.0
                          16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0'
    outputs = none
  []
[]

[VectorPostprocessors]
  [inner_product]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = u
    function = xyzt
    execute_on = 'initial timestep_end'
  []
[]

[Problem]
  solve = false
  kernel_coverage_check = false
  skip_nl_system_check = true
[]

[Executioner]
  type = Transient
  dt = 0.1
  end_time = 1
[]

[Outputs]
  csv = true
  execute_on = final
[]

(modules/combined/test/tests/optimization/invOpt_elasticity_modular/forward.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 11
    ny = 11
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [T]
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      displacements = 'disp_x disp_y'
      [all]
        strain = SMALL
        new_system = true
        formulation = TOTAL
        incremental = true
        volumetric_locking_correction = false
        displacements = 'disp_x disp_y'
      []
    []
  []
[]

[NEML2]
  input = 'elasticity.i'
  verbose = true
  device = 'cpu'
  [all]
    model = 'forward_elasticity_model'

    moose_input_types = 'MATERIAL'
    moose_inputs = 'neml2_strain'
    neml2_inputs = 'forces/E'

    moose_parameter_types = 'MATERIAL'
    moose_parameters = 'E_material'
    neml2_parameters = 'E'

    moose_output_types = 'MATERIAL'
    moose_outputs = 'neml2_stress'
    neml2_outputs = 'state/S'

    moose_derivative_types = 'MATERIAL'
    moose_derivatives = 'neml2_jacobian'
    neml2_derivatives = 'state/S forces/E'
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = bottom
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [top_x]
    type = NeumannBC
    variable = disp_x
    boundary = top
    value = 1.0
  []
  [top_y]
    type = NeumannBC
    variable = disp_y
    boundary = top
    value = 1.0
  []
[]

[Materials]
  [convert_strain]
    type = RankTwoTensorToSymmetricRankTwoTensor
    from = 'mechanical_strain'
    to = 'neml2_strain'
  []
  [stress]
    type = ComputeLagrangianObjectiveCustomSymmetricStress
    custom_small_stress = 'neml2_stress'
    custom_small_jacobian = 'neml2_jacobian'
  []
  [E_material]
    type = GenericFunctionMaterial
    prop_names = 'E_material'
    prop_values = 'E'
  []
[]

[Functions]
  [E]
    type = NearestReporterCoordinatesFunction
    x_coord_name = parametrization/coordx
    y_coord_name = parametrization/coordy
    value_name = parametrization/youngs_modulus
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = disp_x
    objective_name = objective_value
  []
  [parametrization]
    type = ConstantReporter
    real_vector_names = 'coordx coordy youngs_modulus'
    real_vector_values = '0 0 0; ${fparse 8/3} 0 ${fparse -8/3}; 5 5 5'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  # better efficiency if we compute them together
  residual_and_jacobian_together = true
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-14
[]

[Postprocessors]
  [point1]
    type = PointValue
    point = '-1.0 -1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point2]
    type = PointValue
    point = '-1.0 0.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point3]
    type = PointValue
    point = '-1.0 1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point4]
    type = PointValue
    point = '0.0 -1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point5]
    type = PointValue
    point = '0.0  0.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point6]
    type = PointValue
    point = '0.0  1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point7]
    type = PointValue
    point = '1.0 -1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point8]
    type = PointValue
    point = '1.0  0.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
  [point9]
    type = PointValue
    point = '1.0  1.0 0.0'
    variable = disp_x
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = 'forward'
  console = false
[]

(modules/optimization/examples/materialTransient/gradient.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 10
    ny = 10
  []
[]

[Variables/u_adjoint]
  initial_condition = 0
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u_adjoint
  []
  [diff]
    type = MatDiffusion
    variable = u_adjoint
    diffusivity = D
  []
[]

[DiracKernels]
  [misfit]
    type = ReporterTimePointSource
    variable = u_adjoint
    value_name = data/misfit_values
    x_coord_name = data/measurement_xcoord
    y_coord_name = data/measurement_ycoord
    z_coord_name = data/measurement_zcoord
    time_name = data/measurement_time
    reverse_time_end = 1
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u_adjoint
    boundary = 'right top'
    value = 0
  []
[]

[Materials]
  [diffc]
    type = GenericFunctionMaterial
    prop_names = 'D'
    prop_values = 'diffc_fun'
  []
[]

[Functions]
  [diffc_fun]
    type = NearestReporterCoordinatesFunction
    value_name = 'diffc_rep/D_vals'
    x_coord_name = 'diffc_rep/D_x_coord'
    y_coord_name = 'diffc_rep/D_y_coord'
  []
[]

[Reporters]
  [diffc_rep]
    type = ConstantReporter
    real_vector_names = 'D_x_coord D_y_coord D_vals'
    real_vector_values = '0.25 0.75 0.25 0.75;
                          0.25 0.25 0.75 0.75;
                          0.1  10   10   0.1' # Reference solution
    outputs = none
  []
  [data]
    type = OptimizationData
  []
[]

[AuxVariables/u]
[]

[UserObjects]
  [load_u]
    type = AdjointSolutionUserObject
    mesh = forward_out.e
    system_variables = 'u'
    reverse_time_end = 1
    execute_on = 'timestep_begin'
  []
[]

[AuxKernels]
  [u_aux]
    type = SolutionAux
    variable = u
    solution = load_u
    direct = true
    execute_on = 'timestep_begin'
  []
[]

[VectorPostprocessors]
  [adjoint]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = u_adjoint
    forward_variable = u
    function = diffc_fun
    reverse_time_end = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12

  dt = 0.1
  num_steps = 10
[]

(modules/optimization/test/tests/optimizationreporter/bimaterial/model_and_adjoint.i)

# Steady state Heat conduction in a 2D domain with two diffusivities
# The domain is -4 <= x <= 4 and -4 <= y <= 4
# The top-half of the domain (y > 0) has high diffusivity
# The bottom-half of the domain (y < 0) has low diffusivity

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 16
    ny = 16
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
  kernel_coverage_check = false
[]

[Variables]
  [temperature]
  []
  [temperature_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = diffusivity
  []
  [heat_source]
    type = BodyForce
    value = 100
    variable = temperature
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 0
  []
[]

[Functions]
  [diffusivity_function]
    type = NearestReporterCoordinatesFunction
    x_coord_name = data/coordx
    y_coord_name = data/coordy
    value_name = data/diffusivity
  []
[]

[Materials]
  [mat]
    type = GenericFunctionMaterial
    prop_names = diffusivity
    prop_values = diffusivity_function
  []
[]

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = temperature_adjoint
    x_coord_name = measure_data/measurement_xcoord
    y_coord_name = measure_data/measurement_ycoord
    z_coord_name = measure_data/measurement_zcoord
    value_name = measure_data/misfit_values
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
  []
  [data]
    type = ConstantReporter
    real_vector_names = 'coordx coordy diffusivity'
    real_vector_values = '0 0; -2 2; 5 10'
  []
[]

[VectorPostprocessors]
  [gradvec]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = temperature_adjoint
    forward_variable = temperature
    function = diffusivity_function
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Preconditioning]
  [nl0]
    type = SMP
    nl_sys = 'nl0'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
  [adjoint]
    type = SMP
    nl_sys = 'adjoint'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

[Outputs]
  console = false
[]

(modules/optimization/examples/simpleTransient/forward.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    xmax = 1
    ymin = -1
    ymax = 1
  []
[]

[Variables]
  [u]
  []
[]

[VectorPostprocessors]
  [src_values]
    type = CSVReader
    csv_file = source_params.csv
    header = true
    outputs = none
  []
[]

[ICs]
  [initial]
    type = FunctionIC
    variable = u
    function = exact
  []
[]

[Kernels]
  [dt]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    function = source
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = '2*exp(-2.0*(x - sin(2*pi*t))^2)*exp(-2.0*(y - cos(2*pi*t))^2)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/pi'
  []
  [source]
    type = NearestReporterCoordinatesFunction
    x_coord_name = src_values/coordx
    y_coord_name = src_values/coordy
    time_name = src_values/time
    value_name = src_values/values
  []
[]

[Executioner]
  type = Transient

  num_steps = 100
  end_time = 1

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  reuse_preconditioner = true
  reuse_preconditioner_max_linear_its = 50
[]

[Reporters]
  [measured_data]
    type = OptimizationData
    measurement_file = mms_data.csv
    file_xcoord = x
    file_ycoord = y
    file_zcoord = z
    file_time = t
    file_value = u
    variable = u
    execute_on = timestep_end
    objective_name = objective_value
    outputs = none
  []
[]

[Postprocessors]
  [topRight_pp]
    type = PointValue
    point = '0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomRight_pp]
    type = PointValue
    point = '-0.5 0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [bottomLeft_pp]
    type = PointValue
    point = '-0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
  [topLeft_pp]
    type = PointValue
    point = '0.5 -0.5 0'
    variable = u
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  csv = true
  console = false
[]

Overview
Example Input File Syntax
Input Parameters
Input Files