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-f42da2a1-3f81-4fa7-8610-4c48e2dcfdda");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
Controllable:No
Description:The user defined function.
param_symbol_namesNames of parameters in 'expression' being optimized.
C++ Type:std::vector<std::string>
Controllable:No
Description:Names of parameters in 'expression' being optimized.
param_vector_nameReporter or VectorPostprocessor vector containing parameter values.
C++ Type:ReporterName
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>
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>
Controllable:No
Description:Constant numeric values for vars.
execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS.

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/combined/test/tests/invOpt_bc_convective/forward.i)
(modules/combined/test/tests/invOpt_bc_convective/adjoint.i)
(modules/combined/test/tests/invOpt_nonlinear/homogeneous_forward.i)
(modules/optimization/test/tests/optimizationreporter/material/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/nonlinear_material/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/adjoint_nonLinear.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/homogeneous_forward.i)
(modules/combined/test/tests/invOpt_nonlinear/forward.i)
(modules/combined/test/tests/invOpt_nonlinear/adjoint.i)
(modules/combined/test/tests/invOpt_mechanics/forward.i)
(modules/combined/test/tests/invOpt_mechanics/adjoint.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/forward_nonLinear.i)
(modules/optimization/test/tests/functions/parsed_function/parsed_function.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/combined/test/tests/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
    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/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/combined/test/tests/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/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/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]
    nl_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
    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/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
    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/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/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]
    nl_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
  []
[]

[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
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'left right'
    real_vector_values = '0 0; 0' # Dummy
  []
[]

[Outputs]
  console = false
  exodus = true
[]

(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/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/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/combined/test/tests/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
    variable = forwardT
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'heat_source'
    real_vector_values = '0' # Dummy
  []
[]

[Outputs]
  console = false
[]

(modules/combined/test/tests/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/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
    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/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/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
    variable = temperature
  []
  [params]
    type = ConstantReporter
    real_vector_names = 'q'
    real_vector_values = '0' # Dummy value
  []
[]

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

(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
    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/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/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
    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