ParsedOptimizationFunction

Function used for optimization that uses a parsed expression with parameter dependence.

Overview

This function is similar to ParsedFunction except it has some dedicated routines relevant to optimization, particularly the ability to differentiate the function with respect to parameters. The "expression" parameter indicates the function expression. Users may specify x, y, z, and t for space-time dependence. They may also define variables with constant values in the expression by specifying "constant_symbol_names" and "constant_symbol_values" pairs. Finally, parameter variables can be specified which correspond to the definitions in "param_symbol_names". The values of these parameter variables are evaluated from the inputted vector in "param_vector_name". The vector specified in "param_vector_name" can either be a vector-postprocessor vector or a vector reporter value. An error will occur if the length of this vector does not match the number of values specified in "param_symbol_names".

Example Input File Syntax

Here is an example where the parsed function represents the following expression:

var element = document.getElementById("moose-equation-5d93bf07-0cb0-4674-a472-3ba426e665e9");katex.render("f(x,y,z,t; \\vec{v}) = xv_1 + yv_2^2 + zv_3^3 + tv_4^4", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

[Functions]
  [parsed_opt]
    type = ParsedOptimizationFunction
    expression = 'x*v1 + y*v2*v2 + z*v3*v3*v3 + t*v4*v4*v4*v4'
    param_symbol_names = 'v1 v2 v3 v4'
    param_vector_name = 'params/vals'
  []
[]

params/vals is the name of a vector reporter value, define as:

[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    # Random numbers (0,1)
    real_vector_values = '0.2045493861327407 0.1683865411251007 0.5071506764525194 0.7257355264179883'
  []
[]

Input Parameters

expressionThe user defined function.
C++ Type:FunctionExpression
Unit:(no unit assumed)
Controllable:No
Description:The user defined function.
param_symbol_namesNames of parameters in 'expression' being optimized.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Names of parameters in 'expression' being optimized.
param_vector_nameReporter or VectorPostprocessor vector containing parameter values.
C++ Type:ReporterName
Unit:(no unit assumed)
Controllable:No
Description:Reporter or VectorPostprocessor vector containing parameter values.

Required Parameters

constant_symbol_namesVariables (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the symbol_values vector.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Variables (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the symbol_values vector.
constant_symbol_valuesConstant numeric values for vars.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Constant numeric values for vars.

Optional Parameters

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

Advanced Parameters

Input Files

(modules/optimization/test/tests/misc/scaling_test/scaling_test.i)
(modules/optimization/test/tests/outputs/exodus_optimization_steady/adjoint_iteration_output.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/forward.i)
(modules/combined/test/tests/optimization/invOpt_nonlinear/adjoint.i)
(modules/combined/test/tests/optimization/invOpt_bc_convective/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint_nonLinear.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward.i)
(modules/combined/test/tests/optimization/invOpt_bc_convective/forward.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/nonlinear_material/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/function_optimization/forward.i)
(modules/optimization/test/tests/optimizationreporter/material/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward_nonLinear.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/adjoint.i)
(modules/optimization/test/tests/reporters/multiExperiment/forward.i)
(modules/optimization/test/tests/vectorpostprocessors/element_reaction_inner_product/element_reaction_inner_product.i)
(modules/optimization/test/tests/executioners/constrained/shape_optimization/forward.i)
(modules/optimization/test/tests/outputs/exodus_optimization_steady/forward.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint.i)
(modules/optimization/test/tests/functions/parsed_function/parsed_function.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/forward_and_adjoint.i)
(modules/combined/test/tests/optimization/invOpt_nonlinear/homogeneous_forward.i)
(modules/combined/test/tests/optimization/invOpt_nonlinear/forward.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/homogeneous_forward.i)
(modules/optimization/test/tests/executioners/constrained/inequality/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/material/forward.i)

(modules/optimization/test/tests/functions/parsed_function/parsed_function.i)

[Optimization]
[]

[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    # Random numbers (0,1)
    real_vector_values = '0.2045493861327407 0.1683865411251007 0.5071506764525194 0.7257355264179883'
  []
[]

[Functions]
  [parsed_opt]
    type = ParsedOptimizationFunction
    expression = 'x*v1 + y*v2*v2 + z*v3*v3*v3 + t*v4*v4*v4*v4'
    param_symbol_names = 'v1 v2 v3 v4'
    param_vector_name = 'params/vals'
  []
[]

[VectorPostprocessors]
  [test]
    type = OptimizationFunctionTest
    functions = parsed_opt
    # Random numbers (0,1)
    points = '0.1004222428676613 0.21941135757659 0.9310663354302137'
    times = '0.3313593793207535'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/optimization/test/tests/functions/parsed_function/parsed_function.i)

[Optimization]
[]

[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    # Random numbers (0,1)
    real_vector_values = '0.2045493861327407 0.1683865411251007 0.5071506764525194 0.7257355264179883'
  []
[]

[Functions]
  [parsed_opt]
    type = ParsedOptimizationFunction
    expression = 'x*v1 + y*v2*v2 + z*v3*v3*v3 + t*v4*v4*v4*v4'
    param_symbol_names = 'v1 v2 v3 v4'
    param_vector_name = 'params/vals'
  []
[]

[VectorPostprocessors]
  [test]
    type = OptimizationFunctionTest
    functions = parsed_opt
    # Random numbers (0,1)
    points = '0.1004222428676613 0.21941135757659 0.9310663354302137'
    times = '0.3313593793207535'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/optimization/test/tests/misc/scaling_test/scaling_test.i)

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 2
    nz = 1
    xmin = 9.4615
    xmax = 92.0115
    ymin = 3.175
    ymax = 22.225
    zmin = 0.489
    zmax = 0.755
  []
[]

[Variables]
  [T]
    scaling = 10
  []
  [lam_T]
    solver_sys = adjoint
    scaling = 1e3
  []
[]

[Kernels]
  [heat_conduction]
    type = ADMatDiffusion
    variable = T
    diffusivity = thermal_conductivity
  []
  [heat_source]
    type = ADBodyForce
    function = src_fuel_function
    variable = T
  []
[]

[BCs]
  [dir_BC_front]
    type = NeumannBC
    variable = T
    boundary = front
    value = 2
  []
  [dir_BC_back]
    type = DirichletBC
    variable = T
    boundary = back
    value = 300
  []
[]

[Materials]
  # fuel properties
  [fuel_thermal]
    type = ADGenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 17.6e3
  []
[]

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

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu mumps'

  line_search = 'none'

  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-30
  nl_max_its = 10

  l_max_its = 10
[]

##---------Forward Optimization stuff------------------#
[Reporters]
  [measure_data]
    type = ConstantReporter
    real_vector_names = 'x y z u weight'
    real_vector_values = '0.2 0.2 0.0; 0.3 0.8 0.0; 0 0 0; 5 5 5; 1 1 1'
  []
  [params_fuel]
    type = ConstantReporter
    real_vector_names = 'source'
    real_vector_values = '5e7' # Dummy
  []
[]

[Functions]
  [src_fuel_function]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params_fuel/source'
  []
[]
##---------Adjoint Optimization stuff------------------#
[DiracKernels]
  [adjointLoad_T]
    type = ReporterPointSource
    variable = lam_T
    x_coord_name = measure_data/x
    y_coord_name = measure_data/y
    z_coord_name = measure_data/z
    value_name = measure_data/u
  []
[]
##--------- Outputs ------------------#

[Debug]
  show_var_residual_norms = true
[]

(modules/optimization/test/tests/outputs/exodus_optimization_steady/adjoint_iteration_output.i)

[Mesh]
[]

[Variables]
  [adjointVar]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = adjointVar
    diffusivity = thermal_conductivity
  []
[]

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

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'p1'
    real_vector_values = '0' # Dummy value
  []
[]

[AuxVariables]
  [temperature_forward]
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjointVar
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjointVar
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjointVar
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjointVar
    boundary = top
    value = 0
  []
[]

[Functions]
  [thermo_conduct]
    type = ParsedOptimizationFunction
    expression = 'alpha'
    param_symbol_names = 'alpha'
    param_vector_name = 'params/p1'
  []
[]

[Materials]
  [thermalProp]
    type = GenericFunctionMaterial
    prop_names = 'thermal_conductivity'
    prop_values = 'thermo_conduct'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[VectorPostprocessors]
  [adjoint_grad]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = adjointVar
    forward_variable = temperature_forward
    function = thermo_conduct
  []
[]

[Outputs]
  console = false
  file_base = 'adjoint'
  [exodus]
    type = ExodusOptimizationSteady
    execute_on = 'TIMESTEP_END'
  []
[]

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

[Mesh]
[]

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

[Kernels]
  [TensorMechanics]
    use_displaced_mesh = false
    displacements = 'disp_x disp_y'
  []
[]

[BCs]
  [left_ux]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_uy]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0
  []
  [right_fy]
    type = FunctionNeumannBC
    variable = disp_y
    boundary = right
    function = right_fy_func
  []
[]

[Functions]
  [right_fy_func]
    type = ParsedOptimizationFunction
    expression = 'val'
    param_symbol_names = 'val'
    param_vector_name = 'params/right_fy_value'
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 10e3
    poissons_ratio = 0.3
  []
  [strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-8
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [point_sample]
    type = PointValueSampler
    variable = 'disp_y'
    points = '5.0 1.0 0'
    sort_by = x
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = disp_y
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'right_fy_value'
    real_vector_values = '0' # Dummy value
  []
[]

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

(modules/combined/test/tests/optimization/invOpt_nonlinear/adjoint.i)

[Executioner]
  type = Steady
  solve_type = NEWTON
  line_search = none
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  nl_max_its = 100
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Mesh]
[]

[Variables]
  [adjointT]
  []
[]

[AuxVariables]
  [forwardT]
  []
  [dDdTgradT]
    order  = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    thermal_conductivity = 'linearized_conductivity'
    variable = adjointT
  []
  [advection]
    type = LevelSetAdvection
    velocity = dDdTgradT
    variable = adjointT
  []
[]

[AuxKernels]
  [dDdTgradT]
    type = ADFunctorElementalGradientAux
    functor = forwardT
    variable = dDdTgradT
    factor_matprop = 'dDdT'
  []
[]

[Materials]
  [LinearizedConductivity]
    type = ADParsedMaterial
    f_name = 'linearized_conductivity'
    function = '10+500*forwardT'
    args = 'forwardT'
  []
  [dDdT]
    type = ADParsedMaterial
    f_name = 'dDdT'
    function = '500'
    args = 'forwardT'
  []
[]


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

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'heat_source'
    real_vector_values = '0' # Dummy
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjointT
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjointT
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjointT
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjointT
    boundary = top
    value = 0
  []
[]

[VectorPostprocessors]
  [gradient_vpp]
    type = ElementOptimizationSourceFunctionInnerProduct
    function = volumetric_heat_func
    variable = adjointT
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/heat_source'
  []
[]

[Outputs]
  console = false
[]

(modules/combined/test/tests/optimization/invOpt_bc_convective/adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmax = 1
    ymax = 2
  []
[]

[AuxVariables]
  [temperature_forward]
  []
  [T2]
  []
[]

[AuxKernels]
  [TT]
    type = ParsedAux
    args = 'temperature temperature_forward'
    variable = T2
    function = 'temperature*(100-temperature_forward)'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
[]

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

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0' # Dummy value
  []
[]

[BCs]
  [left]
    type = ConvectiveFluxFunction
    variable = temperature
    boundary = 'left'
    T_infinity = 0.0
    coefficient = function1
  []
  [right]
    type = NeumannBC
    variable = temperature
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 0
  []
[]

[Materials]
  [steel]
    type = ADGenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-8
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Functions]
  [function1]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params/vals'
  []
[]

[VectorPostprocessors]
  [adjoint_pt]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = T2
    function = function1
    boundary = left
  []
[]

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

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint_nonLinear.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[Variables]
  [adjoint_T]
  []
[]

[AuxVariables]
  [T]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = adjoint_T
    diffusivity = thermal_conductivity
  []
[]

[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
  []
[]

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'q'
    real_vector_values = '0' # Dummy value
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjoint_T
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjoint_T
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjoint_T
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjoint_T
    boundary = top
    value = 0
  []
[]

[Materials]
  [steel]
    type = ParsedMaterial
    f_name = 'thermal_conductivity'
    function = '.01*T'
    args = 'T'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/q'
  []
[]

[VectorPostprocessors]
  [gradient_vpp]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = adjoint_T
    function = volumetric_heat_func
  []
[]

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

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = thermal_conductivity
  []
  [heat_source]
    type = BodyForce
    function = volumetric_heat_func
    variable = temperature
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = temperature
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temperature
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/q'
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'q'
    real_vector_values = '0' # Dummy value
  []
[]

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

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmax = 1
    ymax = 2
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
[]

[BCs]
  [left]
    type = ConvectiveFluxFunction
    variable = temperature
    boundary = 'left'
    T_infinity = 100.0
    coefficient = function1
  []
  [right]
    type = NeumannBC
    variable = temperature
    boundary = right
    value = -100
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 500
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 600
  []
[]

[Materials]
  [steel]
    type = ADGenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-8
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Functions]
  [function1]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params/vals'
  []
[]

[VectorPostprocessors]
  [vertical]
    type = LineValueSampler
    variable = 'temperature'
    start_point = '0.1 0.0 0.0'
    end_point = '0.1 2.0 0.0'
    num_points = 21
    sort_by = id
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0' # Dummy value
  []
[]

[Outputs]
  csv = true
  exodus = false
  console = false
  file_base = 'forward'
[]

(modules/combined/test/tests/optimization/invOpt_mechanics/adjoint.i)

[Mesh]
[]

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

[Kernels]
  [TensorMechanics]
    use_displaced_mesh = false
    displacements ='disp_x disp_y'
  []
[]

#-----adjoint problem information------------------
[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = disp_y
    x_coord_name = misfit/measurement_xcoord
    y_coord_name = misfit/measurement_ycoord
    z_coord_name = misfit/measurement_zcoord
    value_name = misfit/misfit_values
  []
[]

[Reporters]
  [misfit]
    type=OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'right_fy_value'
    real_vector_values = '0' # Dummy value
  []
[]

[Functions]
  [right_fy_func]
    type = ParsedOptimizationFunction
    expression = 'val'
    param_symbol_names = 'val'
    param_vector_name = 'params/right_fy_value'
  []
[]

[VectorPostprocessors]
  [adjoint_pt]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = disp_y
    function = right_fy_func
    boundary = right
  []
[]

#---------------------------------------------------

[BCs]
  [left_ux]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_uy]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0
  []
  [right_fy]
    type = NeumannBC
    variable = disp_y
    boundary = right
    value = 0 #2000
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 10e3
    poissons_ratio = 0.3
  []
  [strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-8
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

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

(modules/optimization/test/tests/optimizationreporter/nonlinear_material/forward_and_adjoint.i)

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

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

[Variables]
  [forwardT]
  []
  [adjointT]
    solver_sys = adjoint
  []
[]

[Kernels]
  [heat_conduction]
    type = ADMatDiffusion
    variable = forwardT
    diffusivity = 'conductivity'
  []
  [heat_source]
    type = ADBodyForce
    function = volumetric_heat_func
    variable = forwardT
  []
[]

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

[Materials]
  [NonlinearConductivity]
    type = ADParsedMaterial
    property_name = conductivity
    expression = '10+500*forwardT'
    coupled_variables = 'forwardT'
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/heat_source'
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = forwardT
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = forwardT
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = forwardT
    boundary = bottom
    value = 2
  []
  [top]
    type = DirichletBC
    variable = forwardT
    boundary = top
    value = 1
  []
[]

[Reporters]
  [measurement_locations]
    type = OptimizationData
    objective_name = objective_value
    variable = forwardT
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'heat_source'
    real_vector_values = '0' # Dummy
  []
[]

[VectorPostprocessors]
  [gradient_vpp]
    type = ElementOptimizationSourceFunctionInnerProduct
    function = volumetric_heat_func
    variable = adjointT
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  line_search = none
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  console = false
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/function_optimization/forward.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Functions]
  [obj_func]
    type = ParsedOptimizationFunction
    expression = 'pow(x_val + 2 * y_val - 7, 2) + pow(2 * x_val + y_val - 5, 2)'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
  [df_dx]
    type = ParsedOptimizationFunction
    expression = '2 * (x_val + 2 * y_val - 7) + 4 * (2 * x_val + y_val - 5)'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
  [df_dy]
    type = ParsedOptimizationFunction
    expression = '4 * (x_val + 2 * y_val - 7) + 2 * (2 * x_val + y_val - 5)'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
[]

[Postprocessors]
  [obj_pp]
    type = FunctionValuePostprocessor
    function = obj_func
    execute_on = 'INITIAL TIMESTEP_END'
    outputs = console
  []
  [df_dx]
    type = FunctionValuePostprocessor
    function = df_dx
  []
  [df_dy]
    type = FunctionValuePostprocessor
    function = df_dy
  []

[]

[VectorPostprocessors]
  [grad_f]
    type = VectorOfPostprocessors
    postprocessors = 'df_dx df_dy'
  []
[]

[Reporters]
  [vals]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0 4'
  []
[]

(modules/optimization/test/tests/optimizationreporter/material/adjoint.i)

[Mesh]
[]

[Variables]
  [adjointVar]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = adjointVar
    diffusivity = thermal_conductivity
  []
[]

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

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'p1'
    real_vector_values = '0' # Dummy value
  []
[]

[AuxVariables]
  [temperature_forward]
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjointVar
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjointVar
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjointVar
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjointVar
    boundary = top
    value = 0
  []
[]

[Functions]
  [thermo_conduct]
    type = ParsedOptimizationFunction
    expression = 'alpha'
    param_symbol_names = 'alpha'
    param_vector_name = 'params/p1'
  []
[]

[Materials]
  [thermalProp]
    type = GenericFunctionMaterial
    prop_names = 'thermal_conductivity'
    prop_values = 'thermo_conduct'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[VectorPostprocessors]
  [adjoint_grad]
    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
    variable = adjointVar
    forward_variable = temperature_forward
    function = thermo_conduct
  []
[]

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

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward_nonLinear.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[Variables]
  [T]
    initial_condition = 100
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = T
    diffusivity = thermal_conductivity
  []
  [heat_source]
    type = BodyForce
    function = volumetric_heat_func
    variable = T
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = T
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = T
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = T
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = T
    boundary = top
    value = 100
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/q'
  []
[]

[Materials]
  [steel]
    type = ParsedMaterial
    f_name = 'thermal_conductivity'
    function = '.01*T'
    args = 'T'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = T
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'q'
    real_vector_values = '0' # Dummy value
  []
[]

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

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/adjoint.i)

[Mesh]
[]

[Variables]
  [adjoint_T]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = adjoint_T
    diffusivity = thermal_conductivity
  []
[]

[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
    weight_name = misfit/weight
  []
[]

[Reporters]
  [misfit]
    type = OptimizationData
    variable_weight_names = 'weight'
  []
  [params_left]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0 0' # Dummy
  []
  [params_right]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0' # Dummy
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjoint_T
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjoint_T
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjoint_T
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjoint_T
    boundary = top
    value = 0
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  line_search = none
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Functions]
  [left_function]
    type = ParsedOptimizationFunction
    expression = 'a + b*y'
    param_symbol_names = 'a b'
    param_vector_name = 'params_left/vals'
  []
  [right_function]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params_right/vals'
  []
[]

[VectorPostprocessors]
  [grad_bc_left]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = adjoint_T
    function = left_function
    boundary = left
  []
  [grad_bc_right]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = adjoint_T
    function = right_function
    boundary = right
  []
[]

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

(modules/optimization/test/tests/reporters/multiExperiment/forward.i)

omega = 1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Functions]
  [obj_func]
    type = ParsedOptimizationFunction
    expression = 'pow(x_val + 2 * y_val - ${omega}-5, 2) + pow(2 * x_val + y_val - ${omega}, 2)'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
  [df_dx]
    type = ParsedOptimizationFunction
    expression = '2 * (x_val + 2 * y_val - ${omega}-5) + 4 * (2 * x_val + y_val - ${omega})'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
  [df_dy]
    type = ParsedOptimizationFunction
    expression = '4 * (x_val + 2 * y_val - ${omega}-5) + 2 * (2 * x_val + y_val - ${omega})'
    param_symbol_names = 'x_val y_val'
    param_vector_name = vals/vals
  []
[]

[Postprocessors]
  [obj_pp]
    type = FunctionValuePostprocessor
    function = obj_func
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [df_dx]
    type = FunctionValuePostprocessor
    function = df_dx
  []
  [df_dy]
    type = FunctionValuePostprocessor
    function = df_dy
  []
  [omega]
    type = ConstantPostprocessor
    value = ${omega}
  []
[]

[VectorPostprocessors]
  [grad_f]
    type = VectorOfPostprocessors
    postprocessors = 'df_dx df_dy'
  []
[]

[Reporters]
  [vals]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0 0'
  []
[]

[Outputs]
  console = false
[]

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 10
  []
[]

[AuxVariables]
  [u]
  []
  [v]
    initial_condition = 1
  []
  [dp1]
  []
  [dp2]
  []
[]

p1 = 3.14
p2 = 2.72
[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'p'
    real_vector_values = '${p1} ${p2}'
  []
[]

[Functions]
  [p_fun]
    type = ParsedOptimizationFunction
    expression = 'p_1*x + p_2*p_2'
    param_symbol_names = 'p_1 p_2'
    param_vector_name = params/p
  []
  [u_fun]
    type = ParsedFunction
    expression = 'x'
  []
  [dp1_fun]
    type = ParsedFunction
    expression = 'x'
    symbol_names = 'p_1 p_2'
    symbol_values = '${p1} ${p2}'
  []
  [dp2_fun]
    type = ParsedFunction
    expression = '2*p_2'
    symbol_names = 'p_1 p_2'
    symbol_values = '${p1} ${p2}'
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    variable = u
    function = u_fun
  []
  [dp1_ic]
    type = FunctionIC
    variable = dp1
    function = dp1_fun
  []
  [dp2_ic]
    type = FunctionIC
    variable = dp2
    function = dp2_fun
  []
[]

[VectorPostprocessors]
  [inner_product]
    type = ElementOptimizationReactionFunctionInnerProduct
    forward_variable = u
    variable = v
    function = p_fun
    execute_on = initial
  []
[]

[Postprocessors]
  [udp1v]
    type = VectorPostprocessorComponent
    vectorpostprocessor = inner_product
    vector_name = inner_product
    index = 0
  []
  [udp2v]
    type = VectorPostprocessorComponent
    vectorpostprocessor = inner_product
    vector_name = inner_product
    index = 1
  []
  [udp1v_exact]
    type = VariableInnerProduct
    variable = u
    second_variable = dp1
  []
  [udp2v_exact]
    type = VariableInnerProduct
    variable = u
    second_variable = dp2
  []
  [compare]
    type = ParsedPostprocessor
    expression = 'abs(udp1v + udp1v_exact) + abs(udp2v + udp2v_exact)'
    pp_names = 'udp1v udp2v udp1v_exact udp2v_exact'
  []
[]

[UserObjects]
  [terminate]
    type = Terminator
    expression = 'compare > 1e-8'
    error_level = ERROR
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

(modules/optimization/test/tests/executioners/constrained/shape_optimization/forward.i)

# This test is documented as an example for ConstrainedShapeOptimization. This
# test should not be changed without updating the documentation.

inner_radius = 6
outer_radius = 10
volume_constraint = 200

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [mesh]
    type = ConcentricCircleMeshGenerator
    has_outer_square = no
    num_sectors = 16
    radii = '${inner_radius} ${outer_radius}'
    rings = '16 16'
    preserve_volumes = false
  []
  [inner_radius]
    type = SideSetsBetweenSubdomainsGenerator
    input = mesh
    new_boundary = inner
    primary_block = 2
    paired_block = 1
  []

  [delete]
    type = BlockDeletionGenerator
    input = inner_radius
    block = 1
  []
  [gather_all]
    type = BoundingBoxNodeSetGenerator
    input = delete
    bottom_left = '-100 -100 -100'
    top_right = '100 100 100'
    new_boundary = total
  []
  [combine]
    type = SideSetsFromBoundingBoxGenerator
    input = gather_all
    bottom_left = '-100 -100 -100'
    top_right = '100 100 100'
    boundaries_old = 'inner outer'
    boundary_new = moving
  []

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

[AuxVariables]
  [dist_between]
    [AuxKernel]
      type = NearestNodeDistanceAux
      variable = dist_between
      paired_boundary = moving
      boundary = total
      block = 2
      use_displaced_mesh = false
      execute_on = "INITIAL"
    []
  []
[]

[Kernels]
  [disp_x]
    type = MatDiffusion
    variable = disp_x
    use_displaced_mesh = false
    diffusivity = diff_coef
  []
  [disp_y]
    type = MatDiffusion
    variable = disp_y
    use_displaced_mesh = false
    diffusivity = diff_coef
  []
  # run physics of interest on deformed mesh
  [Diffusion]
    type = FunctionDiffusion
    variable = T
    use_displaced_mesh = true
  []
  [Source]
    type = BodyForce
    variable = T
    value = 1
    use_displaced_mesh = true
  []
[]

[Materials]
  # perserve elements near the boundary
  [diff_coef]
    type = ParsedMaterial
    coupled_variables = 'dist_between'
    expression = '1/(dist_between+0.5)'
    property_name = 'diff_coef'
  []
  [h]
    type = ADGenericFunctionMaterial
    prop_names = h
    prop_values = h
  []
  # convection type boundary condition
  [convection_bc]
    type = ADParsedMaterial
    coupled_variables = "T"
    expression = "h*(100-T)"
    material_property_names = "h"
    property_name = convection
  []
[]

[Functions]
  [r1_x]
    type = ParsedOptimizationFunction
    expression = 'r1 * cos((atan(y/x)))'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [r1_y]
    type = ParsedOptimizationFunction
    expression = 'r1 * sin((atan(y/x)))'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [r0_x]
    type = ParsedOptimizationFunction
    expression = 'r0 * cos((atan(y/x)))'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [r0_y]
    type = ParsedOptimizationFunction
    expression = 'r0 * sin((atan(y/x)))'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [h]
    type = ParsedOptimizationFunction
    # r0+${inner_radius} is the true current inner radius
    expression = '10 /(pi * (r0+${inner_radius})^3)'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [eq_grad_r0]
    type = ParsedOptimizationFunction
    expression = '-2 * pi * (r0 + ${inner_radius})'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
  [eq_grad_r1]
    type = ParsedOptimizationFunction
    # r1+${outer_radius} is the true current outer radius
    expression = '2 * pi * (r1+${outer_radius})'
    param_symbol_names = 'r0 r1'
    param_vector_name = 'params/radii'
  []
[]

[BCs]
  [diffuse_r1_x]
    type = ADFunctionDirichletBC
    variable = disp_x
    boundary = 'outer'
    function = r1_x
    preset = false
  []
  [diffuse_r1_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = 'outer'
    function = r1_y
    preset = false
  []
  [diffuse_r0_x]
    type = ADFunctionDirichletBC
    variable = disp_x
    boundary = 'inner'
    function = r0_x
    preset = false
  []
  [diffuse_r0_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = 'inner'
    function = r0_y
    preset = false
  []
  # run physics on deformed mesh
  [convection]
    type = ADMatNeumannBC
    variable = T
    boundary = inner
    boundary_material = convection
    use_displaced_mesh = true
    value = 1
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'radii'
    real_vector_values = '0 0'
    dof_id_type_vector_names = 'num_params'
    dof_id_type_vector_values = '2'
  []
[]

[Postprocessors]
  [current_volume]
    type = VolumePostprocessor
    use_displaced_mesh = true
  []
  # objective function
  [objective]
    type = NodalExtremeValue
    variable = T
  []
  [eq_constraint]
    type = ParsedPostprocessor
    pp_names = current_volume
    expression = 'current_volume - ${volume_constraint}'
  []
  [func_r0]
    type = FunctionValuePostprocessor
    function = eq_grad_r0
  []
  [func_r1]
    type = FunctionValuePostprocessor
    function = eq_grad_r1
  []
[]

[VectorPostprocessors]
  # convert "Real" postprocessors to vectors
  [vol_constraint]
    type = VectorOfPostprocessors
    postprocessors = 'eq_constraint'
    force_postaux = true
  []
  [eq_grad]
    type = VectorOfPostprocessors
    postprocessors = 'func_r0 func_r1'
    force_postaux = true
  []
[]

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

[Outputs]
  console = false
[]

(modules/optimization/test/tests/outputs/exodus_optimization_steady/forward.i)

[Mesh]
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = thermal_conductivity
  []
  [heat_source]
    type = BodyForce
    value = 1000
    variable = temperature
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = temperature
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temperature
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [thermo_conduct]
    type = ParsedOptimizationFunction
    expression = 'alpha'
    param_symbol_names = 'alpha'
    param_vector_name = 'params/p1'
  []
[]

[Materials]
  [steel]
    type = GenericFunctionMaterial
    prop_names = 'thermal_conductivity'
    prop_values = 'thermo_conduct'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
    outputs = none
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'p1'
    real_vector_values = '0' # Dummy value
  []
[]

[Outputs]
  console = false
  file_base = 'forward'
  [exo]
    type = ExodusOptimizationSteady
    execute_on = 'TIMESTEP_END'
  []
[]

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward.i)

[Mesh]
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = thermal_conductivity
  []
[]

[BCs]
  [left]
    type = FunctionNeumannBC
    variable = temperature
    boundary = left
    function = left_function
  []
  [right]
    type = FunctionNeumannBC
    variable = temperature
    boundary = right
    function = right_function
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [left_function]
    type = ParsedOptimizationFunction
    expression = 'a + b*y'
    param_symbol_names = 'a b'
    param_vector_name = 'params_left/vals'
  []
  [right_function]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params_right/vals'
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  line_search = none
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[VectorPostprocessors]
  [vertical_1]
    type = LineValueSampler
    variable = 'temperature'
    start_point = '0.2 0.0 0'
    end_point = '0.2 2.0 0'
    num_points = 21
    sort_by = y
  []
  [vertical_2]
    type = LineValueSampler
    variable = 'temperature'
    start_point = '0.8 0.0 0'
    end_point = '0.8 2.0 0'
    num_points = 21
    sort_by = y
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    objective_name = objective_value
    variable_weight_names = weightForTemperature
  []
  [params_left]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0 0' # Dummy
  []
  [params_right]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0' # Dummy
  []
[]

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

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[Variables]
  [adjoint_T]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = adjoint_T
    diffusivity = thermal_conductivity
  []
[]

[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
  []
[]

[Reporters]
  [misfit]
    type = OptimizationData
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'q'
    real_vector_values = '0' # Dummy value
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = adjoint_T
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = adjoint_T
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = adjoint_T
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = adjoint_T
    boundary = top
    value = 0
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/q'
  []
[]

[VectorPostprocessors]
  [gradient_vpp]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = adjoint_T
    function = volumetric_heat_func
  []
[]

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

(modules/optimization/test/tests/functions/parsed_function/parsed_function.i)

[Optimization]
[]

[Reporters]
  [params]
    type = ConstantReporter
    real_vector_names = 'vals'
    # Random numbers (0,1)
    real_vector_values = '0.2045493861327407 0.1683865411251007 0.5071506764525194 0.7257355264179883'
  []
[]

[Functions]
  [parsed_opt]
    type = ParsedOptimizationFunction
    expression = 'x*v1 + y*v2*v2 + z*v3*v3*v3 + t*v4*v4*v4*v4'
    param_symbol_names = 'v1 v2 v3 v4'
    param_vector_name = 'params/vals'
  []
[]

[VectorPostprocessors]
  [test]
    type = OptimizationFunctionTest
    functions = parsed_opt
    # Random numbers (0,1)
    points = '0.1004222428676613 0.21941135757659 0.9310663354302137'
    times = '0.3313593793207535'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/combined/test/tests/optimization/invOpt_mechanics/forward_and_adjoint.i)

# DO NOT CHANGE THIS TEST
# this test is documented as an example in forceInv_NeumannBC.md
# if this test is changed, the figures will need to be updated.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 2
  xmin = 0.0
  xmax = 5.0
  ymin = 0.0
  ymax = 1.0
  use_displaced_mesh = false
[]

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

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      displacements = 'disp_x disp_y'
      [all]
        displacements = 'disp_x disp_y'
        strain = SMALL
      []
    []
  []
[]

[BCs]
  [left_ux]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_uy]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0
  []
  [right_fy]
    type = FunctionNeumannBC
    variable = disp_y
    boundary = right
    function = right_fy_func
  []
  [right_fx]
    type = FunctionNeumannBC
    variable = disp_x
    boundary = right
    function = right_fx_func
  []
[]

[Functions]
  [right_fy_func]
    type = ParsedOptimizationFunction
    expression = 'val_y'
    param_symbol_names = 'val_x val_y'
    param_vector_name = 'params/right_values'
  []
  [right_fx_func]
    type = ParsedOptimizationFunction
    expression = 'val_x'
    param_symbol_names = 'val_x val_y'
    param_vector_name = 'params/right_values'
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 10e3
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-8
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [point_sample]
    type = PointValueSampler
    variable = 'disp_x disp_y'
    points = '5.0 1.0 0'
    sort_by = x
  []
[]

[Reporters]
  [measure_data_x]
    type = OptimizationData
    objective_name = objective_value
    variable = disp_x
    measurement_points = '5.0 1.0 0.0'
    measurement_values = '-13.00873469088'
  []
  [measure_data_y]
    type = OptimizationData
    objective_name = objective_value
    variable = disp_y
    measurement_points = '5.0 1.0 0.0'
    measurement_values = '85.008027719915'
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'right_values'
    real_vector_values = '-1300 2100 ' # True Values
  []
  [combined]
    type = ParsedVectorReporter
    name = gradient
    reporter_names = 'adjoint_pt_x/inner_product adjoint_pt_y/inner_product'
    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
  []
  [obj]
    type = ParsedScalarReporter
    name = obj_val
    reporter_names = 'measure_data_x/objective_value
    measure_data_y/objective_value'
    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
  []
[]

[Outputs]
  csv = false
  console = false
  exodus = false
  file_base = 'forward'
  execute_on = 'FINAL'
  json = false
[]

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

[Variables]
  [adjoint_x]
    initial_condition = 0
    solver_sys = adjoint
    outputs = none
  []
  [adjoint_y]
    initial_condition = 0
    solver_sys = adjoint
    outputs = none
  []
[]

[DiracKernels]
  [pt_x]
    type = ReporterPointSource
    variable = adjoint_x
    x_coord_name = measure_data_x/measurement_xcoord
    y_coord_name = measure_data_x/measurement_ycoord
    z_coord_name = measure_data_x/measurement_zcoord
    value_name = measure_data_x/misfit_values
  []
  [pt_y]
    type = ReporterPointSource
    variable = adjoint_y
    x_coord_name = measure_data_y/measurement_xcoord
    y_coord_name = measure_data_y/measurement_ycoord
    z_coord_name = measure_data_y/measurement_zcoord
    value_name = measure_data_y/misfit_values
  []
[]

[VectorPostprocessors]
  [adjoint_pt_x]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = adjoint_x
    function = right_fx_func
    boundary = right
    execute_on = ADJOINT_TIMESTEP_END
  []
  [adjoint_pt_y]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = adjoint_y
    function = right_fy_func
    boundary = right
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

(modules/combined/test/tests/optimization/invOpt_nonlinear/homogeneous_forward.i)

[Executioner]
  type = Steady
  solve_type = NEWTON
  line_search = none
  #nl_forced_its = 1
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Mesh]
[]

[Variables]
  [T]
  []
[]

[AuxVariables]
  [forwardT]
  []
  [_dDdTgradT]
    order  = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    thermal_conductivity = 'linearized_conductivity'
    variable = T
  []
  [heat_source]
    type = ADMatHeatSource
    material_property = 'volumetric_heat'
    variable = T
  []
  [advection]
    type = ConservativeAdvection
    velocity = _dDdTgradT
    variable = T
    upwinding_type = full  #Full upwinding gives somewhat better results
  []
[]

[AuxKernels]
  [_dDdTgradT]
    type = ADFunctorElementalGradientAux
    functor = forwardT
    variable = _dDdTgradT
    factor_matprop = '_dDdT'
  []
[]

[Materials]
  [LinearizedConductivity]
    type = ADParsedMaterial
    f_name = 'linearized_conductivity'
    function = '10+500*forwardT'
    args = 'forwardT'
  []
  [_dDdT]
    type = ADParsedMaterial
    f_name = '_dDdT' # "_" represents negation
    function = '-500'
    args = 'forwardT'
  []
  [volumetric_heat]
    type = ADGenericFunctionMaterial
    prop_names = 'volumetric_heat'
    prop_values = 'volumetric_heat_func'
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/heat_source'
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = T
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = T
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = T
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = T
    boundary = top
    value = 0
  []
[]

[Reporters]
  [measurement_locations]
    type = OptimizationData
    variable = T
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'heat_source'
    real_vector_values = '0' # Dummy
  []
[]

[Outputs]
  console = false
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  line_search = none
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Mesh]
[]

[Variables]
  [forwardT]
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    thermal_conductivity = 'conductivity'
    variable = forwardT
  []
  [heat_source]
    type = ADMatHeatSource
    material_property = 'volumetric_heat'
    variable = forwardT
  []
[]

[Materials]
  [NonlinearConductivity]
    type = ADParsedMaterial
    f_name = 'conductivity'
    function = '10+500*forwardT'
    args = 'forwardT'
  []
  [volumetric_heat]
    type = ADGenericFunctionMaterial
    prop_names = 'volumetric_heat'
    prop_values = 'volumetric_heat_func'
  []
[]

[Functions]
  [volumetric_heat_func]
    type = ParsedOptimizationFunction
    expression = q
    param_symbol_names = 'q'
    param_vector_name = 'params/heat_source'
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = forwardT
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = forwardT
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = forwardT
    boundary = bottom
    value = 2
  []
  [top]
    type = DirichletBC
    variable = forwardT
    boundary = top
    value = 1
  []
[]

[Reporters]
  [measurement_locations]
    type = OptimizationData
    objective_name = objective_value
    variable = forwardT
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'heat_source'
    real_vector_values = '0' # Dummy
  []
[]

[Outputs]
  console = false
[]

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/homogeneous_forward.i)

[Mesh]
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = thermal_conductivity
  []
[]

[BCs]
  [left]
    type = FunctionNeumannBC
    variable = temperature
    boundary = left
    function = left_function
  []
  [right]
    type = FunctionNeumannBC
    variable = temperature
    boundary = right
    function = right_function
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 0
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 0
  []
[]

[Functions]
  [left_function]
    type = ParsedOptimizationFunction
    expression = 'a + b*y'
    param_symbol_names = 'a b'
    param_vector_name = 'params_left/vals'
  []
  [right_function]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params_right/vals'
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = Steady
  line_search = none
  solve_type = NEWTON
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[VectorPostprocessors]
  [vertical_1]
    type = LineValueSampler
    variable = 'temperature'
    start_point = '0.2 0.0 0'
    end_point = '0.2 2.0 0'
    num_points = 21
    sort_by = y
  []
  [vertical_2]
    type = LineValueSampler
    variable = 'temperature'
    start_point = '0.8 0.0 0'
    end_point = '0.8 2.0 0'
    num_points = 21
    sort_by = y
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable_weight_names = weightForTemperature
    variable = temperature
  []
  [params_left]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0 0' # Dummy
  []
  [params_right]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '0' # Dummy
  []
[]

[Outputs]
  console = false
  exodus = false
  file_base = 'homogenous'
[]

(modules/optimization/test/tests/executioners/constrained/inequality/forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmax = 1
    ymax = 1
  []
[]

[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 = thermal_conductivity
  []
[]

[BCs]
  [left]
    type = FunctionNeumannBC
    variable = temperature
    boundary = left
    function = left_function
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [left_function]
    type = ParsedOptimizationFunction
    expression = 'a + b*y'
    param_symbol_names = 'a b'
    param_vector_name = 'params/left'
  []
  [dc_db]
    type = ParsedFunction
    expression = 'y'
  []

[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  line_search = none
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[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
  []
[]

[VectorPostprocessors]
  [grad_bc_left]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = temperature_adjoint
    function = left_function
    boundary = left
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Postprocessors]
  [sum]
    type = FunctionSideIntegral
    boundary = left
    function = left_function
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    objective_name = objective_value
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'left'
    real_vector_values = '0 0' # Dummy
    execute_on = NONE
  []

[]

[Outputs]
  console = false
  exodus = false
  json = true
[]

#---------Inequality constraints------------#

[VectorPostprocessors]
  [gradient_c]
    type = VectorOfPostprocessors
    postprocessors = 'dc_da dc_db'
  []
  [ineq]
    type = VectorOfPostprocessors
    postprocessors = 'constraint'
  []
[]

[Postprocessors]
  [constraint]
    type = ParsedPostprocessor
    expression = '150 - sum' # 150 is the constraint we want to satisfy
    pp_names = sum
  []
  [dc_da]
    type = FunctionSideIntegral
    boundary = left
    function = -1
  []
  [dc_db]
    type = FunctionSideIntegral
    boundary = left
    function = '-y'
  []
[]

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmax = 1
    ymax = 2
    bias_x = 1.1
    bias_y = 1.1
  []
[]

[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 = thermal_conductivity
  []
[]

[BCs]
  [left]
    type = FunctionNeumannBC
    variable = temperature
    boundary = left
    function = left_function
  []
  [right]
    type = FunctionNeumannBC
    variable = temperature
    boundary = right
    function = right_function
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [left_function]
    type = ParsedOptimizationFunction
    expression = 'a + b*y'
    param_symbol_names = 'a b'
    param_vector_name = 'params/left'
  []
  [right_function]
    type = ParsedOptimizationFunction
    expression = 'a'
    param_symbol_names = 'a'
    param_vector_name = 'params/right'
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  line_search = none
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[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
    weight_name = measure_data/weight
  []
[]

[VectorPostprocessors]
  [grad_bc_left]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = temperature_adjoint
    function = left_function
    boundary = left
    execute_on = ADJOINT_TIMESTEP_END
  []
  [grad_bc_right]
    type = SideOptimizationNeumannFunctionInnerProduct
    variable = temperature_adjoint
    function = right_function
    boundary = right
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    measurement_file = 'measurementData.csv'
    file_xcoord = 'coordx'
    file_ycoord ='y'
    file_zcoord = 'z'
    file_value = 'weightedMeasurement'
    file_variable_weights = 'weight'
    variable_weight_names = 'weight'
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'left right'
    real_vector_values = '0 0; 0' # Dummy
  []
  [vector_sqsum]
    type = ParsedVectorRealReductionReporter
    name = sqsum
    reporter_name= 'measure_data/misfit_values'
    initial_value = 0
    expression = 'reduction_value+indexed_value*indexed_value'
    outputs=none
  []
  [obj_sum]
    type = ParsedScalarReporter
    name = value
    reporter_names = 'vector_sqsum/sqsum'
    reporter_symbols = 'a'
    expression = '0.5*a'
  []
[]

[Outputs]
  console = false
  exodus = true
[]

(modules/optimization/test/tests/optimizationreporter/material/forward.i)

[Mesh]
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = MatDiffusion
    variable = temperature
    diffusivity = thermal_conductivity
  []
  [heat_source]
    type = BodyForce
    value = 1000
    variable = temperature
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = temperature
    boundary = left
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temperature
    boundary = right
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 200
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 100
  []
[]

[Functions]
  [thermo_conduct]
    type = ParsedOptimizationFunction
    expression = 'alpha'
    param_symbol_names = 'alpha'
    param_vector_name = 'params/p1'
  []
[]

[Materials]
  [steel]
    type = GenericFunctionMaterial
    prop_names = 'thermal_conductivity'
    prop_values = 'thermo_conduct'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'p1'
    real_vector_values = '0' # Dummy value
  []
[]

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

Overview
Example Input File Syntax
Input Parameters
Input Files