SteadyAndAdjoint

Executioner for evaluating steady-state simulations and their adjoint.

Overview

This executioner can be used to solve a steady-state forward problem with its adjoint. The forward solve is performed the same way as in Steady, but with the "solve_type" set to NEWTON. This performs the nonlinear iteration in the form:

var element = document.getElementById("moose-equation-f20da355-70e7-41af-a931-35f8d2ecb663");katex.render("\\mathbf{J}(\\mathbf{u}^{i-1}) \\delta \\mathbf{u}^{i} = \\mathbf{R}(\\mathbf{u}^{i-1}), i=1,...,I,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-1fac20b3-78c4-4b24-ba87-50d3ca7da3eb");katex.render("I", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the number of iterations it took to converge the problem. The adjoint problem is then defined as:

var element = document.getElementById("moose-equation-b154e2cd-b470-486d-a280-e8b1e3600173");katex.render("\\mathbf{J}^{\\top}(\\mathbf{u}^{I})\\lambda = -\\mathbf{R}_{\\lambda},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-93a29792-a966-46cf-9aab-d371aa8b7154");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the adjoint solution, $var element = document.getElementById("moose-equation-476f9b35-ff35-4f2a-bf4e-20de445e7567");katex.render("\\mathbf{R}_{\\lambda}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the residual of the adjoint system with $var element = document.getElementById("moose-equation-15a5911d-1733-43a6-a734-8eb2dc6e209a");katex.render("\\lambda\\equiv 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-6c2f838e-be2b-4cdd-9312-be087fe70d35");katex.render("\\mathbf{J}^{\\top}(\\mathbf{u}^{I})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the transpose of the forward system's Jacobian evaluated with the converged forward solution. The adjoint system is basically a linearized and homogenized version of the forward problem with it's own definition of sources.

In order to accurately define the adjoint system, the fully consistent Jacobian must be evaluated. As such, the computeQpJacobian routines in the forward problem kernels must be accurately defined or Automatic Differentiation must be used. Consider using the Jacobian debugger to ensure the Jacobian is computed accurately.

Example Input File Syntax

Solving Adjoint Problems

The first step is to add an adjoint nonlinear system using the "nl_sys_names" parameter in the Problem input block. It is convenient to define the forward system as nl0.

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

Next we need to add an adjoint variable for each forward variable, which is associated with the adjoint system:

Single adjoint variable

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

Multiple adjoint variables

[Variables]
  [u]
  []
  [v]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
  [v_adjoint]
    solver_sys = adjoint
  []
[]

Array adjoint variables

[Variables]
  [u]
    components = 2
  []
  [u_adjoint]
    components = 2
    solver_sys = adjoint
  []
[]

Next we add kernels and BCs associated with the forward and adjoint variables. Only source-like kernels should be added to the adjoint variables like BodyForce, ConstantPointSource, or NeumannBC.

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 1
  []
  [neumann]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
[]

For nonlinear, problems one should use AD Kernels, BCs, and Materials.

[Kernels]
  [diff]
    type = ADMatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = ADBodyForce
    variable = u
    value = 1
  []

  [src_adjoint]
    type = ADBodyForce
    variable = u_adjoint
    value = 1
  []
[]

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

[Materials]
  [diffc]
    type = ADParsedMaterial
    property_name = D
    expression = '0.1 + 5 * u'
    coupled_variables = 'u'
  []
[]

Finally, we will add this executioner and set the forward/adjoint system tags. Note that the tolerance for the adjoint system solve is set solely by linear solver parameters like "l_tol", "l_abs_tol", and "l_max_its".

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

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

Utilization in Gradient-Based Optimization

Utilizing this executioner for gradient-based optimization is quite powerful since the adjoint used to compute the gradient is automatically assembled with this executioner, given that the forward problem Jacobian can be fully constructed.

To include the source for the adjoint problem, the ReporterPointSource can be used to add the simulation misfit from the forward solve, which is calculated in OptimizationData.

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

[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
  []
[]

The gradient can then be computed using an inner-product vector-postprocessor like ElementOptimizationSourceFunctionInnerProduct. Note that these vector-postprocessors must be executed on ADJOINT_TIMESTEP_END which occurs after the adjoint system is solved.

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

The driving optimize app will thus have only have a single FullSolveMultiApp which then transfers both the simulation data (for the objective evaluation) and the inner products (for the gradient evaluation).

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/heat_source'
    to_reporters = 'measurement_locations/measurement_xcoord
                    measurement_locations/measurement_ycoord
                    measurement_locations/measurement_zcoord
                    measurement_locations/measurement_time
                    measurement_locations/measurement_values
                    params/heat_source'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measurement_locations/objective_value
                      gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_heat_source'
  []
[]

Input Parameters

adjoint_systemName of the system representing the adjoint problem.
C++ Type:NonlinearSystemName
Unit:(no unit assumed)
Controllable:No
Description:Name of the system representing the adjoint problem.
forward_systemName of the system representing the forward problem.
C++ Type:NonlinearSystemName
Unit:(no unit assumed)
Controllable:No
Description:Name of the system representing the forward problem.

Required Parameters

time0System time
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:System time
verboseFalseSet to true to print additional information
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to true to print additional information

Optional Parameters

accept_on_max_fixed_point_iterationFalseTrue to treat reaching the maximum number of fixed point iterations as converged.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to treat reaching the maximum number of fixed point iterations as converged.
auto_advanceFalseWhether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
custom_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
custom_ppPostprocessor for custom fixed point convergence check.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor for custom fixed point convergence check.
custom_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
direct_pp_valueFalseTrue to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
disable_fixed_point_residual_norm_checkFalseDisable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Disable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
fixed_point_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
fixed_point_algorithmpicardThe fixed point algorithm to converge the sequence of problems.
Default:picard
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:picard, secant, steffensen
Controllable:No
Description:The fixed point algorithm to converge the sequence of problems.
fixed_point_force_normsFalseForce the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Force the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
fixed_point_max_its1Specifies the maximum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Specifies the maximum number of fixed point iterations.
fixed_point_min_its1Specifies the minimum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Specifies the minimum number of fixed point iterations.
fixed_point_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
relaxation_factor1Fraction of newly computed value to keep.Set between 0 and 2.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of newly computed value to keep.Set between 0 and 2.
transformed_postprocessorsList of main app postprocessors to transform during fixed point iterations
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:List of main app postprocessors to transform during fixed point iterations
transformed_variablesList of main app variables to transform during fixed point iterations
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:List of main app variables to transform during fixed point iterations

Fixed Point Iterations Parameters

automatic_scalingFalseWhether to use automatic scaling for the variables.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to use automatic scaling for the variables.
compute_scaling_onceTrueWhether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step.
ignore_variables_for_autoscalingList of variables that do not participate in autoscaling.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:List of variables that do not participate in autoscaling.
off_diagonals_in_auto_scalingFalseWhether to consider off-diagonals when determining automatic scaling factors.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to consider off-diagonals when determining automatic scaling factors.
resid_vs_jac_scaling_param0A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling
scaling_group_variablesName of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon)
C++ Type:std::vector<std::vector<std::string>>
Unit:(no unit assumed)
Controllable:No
Description:Name of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon)

Solver Variable Scaling Parameters

contact_line_search_allowed_lambda_cuts2The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
Default:2
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
contact_line_search_ltolThe linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
line_searchdefaultSpecifies the line search type (Note: none = basic)
Default:default
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:basic, bt, contact, cp, default, l2, none, project, shell
Controllable:No
Description:Specifies the line search type (Note: none = basic)
line_search_packagepetscThe solver package to use to conduct the line-search
Default:petsc
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:petsc, moose
Controllable:No
Description:The solver package to use to conduct the line-search

Solver Line Search 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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
skip_exception_checkFalseSpecifies whether or not to skip exception check
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Specifies whether or not to skip exception check

Advanced Parameters

l_abs_tol1e-50Linear Absolute Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Absolute Tolerance
l_max_its10000Max Linear Iterations
Default:10000
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Linear Iterations
l_tol1e-05Linear Relative Tolerance
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Relative Tolerance
reuse_preconditionerFalseIf true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
reuse_preconditioner_max_linear_its25Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number
Default:25
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number

Linear Solver Parameters

max_xfem_update4294967295Maximum number of times to update XFEM crack topology in a step due to evolving cracks
Default:4294967295
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Maximum number of times to update XFEM crack topology in a step due to evolving cracks
update_xfem_at_timestep_beginFalseShould XFEM update the mesh at the beginning of the timestep
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Should XFEM update the mesh at the beginning of the timestep

Xfem Fixed Point Iterations Parameters

mffd_typewpSpecifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
Default:wp
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:wp, ds
Controllable:No
Description:Specifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
petsc_optionsSingleton PETSc options
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:-dm_moose_print_embedding, -dm_view, -ksp_converged_reason, -ksp_gmres_modifiedgramschmidt, -ksp_monitor, -ksp_monitor_snes_lg-snes_ksp_ew, -ksp_snes_ew, -snes_converged_reason, -snes_ksp, -snes_ksp_ew, -snes_linesearch_monitor, -snes_mf, -snes_mf_operator, -snes_monitor, -snes_test_display, -snes_view
Controllable:No
Description:Singleton PETSc options
petsc_options_inameNames of PETSc name/value pairs
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:-ksp_atol, -ksp_gmres_restart, -ksp_max_it, -ksp_pc_side, -ksp_rtol, -ksp_type, -mat_fd_coloring_err, -mat_fd_type, -mat_mffd_type, -pc_asm_overlap, -pc_factor_levels, -pc_factor_mat_ordering_type, -pc_hypre_boomeramg_grid_sweeps_all, -pc_hypre_boomeramg_max_iter, -pc_hypre_boomeramg_strong_threshold, -pc_hypre_type, -pc_type, -snes_atol, -snes_linesearch_type, -snes_ls, -snes_max_it, -snes_rtol, -snes_divergence_tolerance, -snes_type, -sub_ksp_type, -sub_pc_type
Controllable:No
Description:Names of PETSc name/value pairs
petsc_options_valueValues of PETSc name/value pairs (must correspond with "petsc_options_iname"
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Values of PETSc name/value pairs (must correspond with "petsc_options_iname"

Petsc Parameters

n_max_nonlinear_pingpong100The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut
Default:100
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut
nl_abs_div_tol1e+50Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
Default:1e+50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
nl_abs_step_tol0Nonlinear Absolute step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute step Tolerance
nl_abs_tol1e-50Nonlinear Absolute Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Tolerance
nl_div_tol1e+10Nonlinear Relative Divergence Tolerance. A negative value disables this check.
Default:1e+10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Divergence Tolerance. A negative value disables this check.
nl_forced_its0The Number of Forced Nonlinear Iterations
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The Number of Forced Nonlinear Iterations
nl_max_funcs10000Max Nonlinear solver function evaluations
Default:10000
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Nonlinear solver function evaluations
nl_max_its50Max Nonlinear Iterations
Default:50
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Nonlinear Iterations
nl_rel_step_tol0Nonlinear Relative step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative step Tolerance
nl_rel_tol1e-08Nonlinear Relative Tolerance
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Tolerance
num_grids1The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
residual_and_jacobian_togetherFalseWhether to compute the residual and Jacobian together.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute the residual and Jacobian together.
snesmf_reuse_baseTrueSpecifies whether or not to reuse the base vector for matrix-free calculation
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Specifies whether or not to reuse the base vector for matrix-free calculation
splittingTop-level splitting defining a hierarchical decomposition into subsystems to help the solver.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Top-level splitting defining a hierarchical decomposition into subsystems to help the solver.
use_pre_SMO_residualFalseCompute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Compute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.

Nonlinear Solver Parameters

Restart Parameters

Input Files

(modules/optimization/test/tests/outputs/exodus_optimization_steady/forward_and_adjoint_iteration_output.i)
(modules/optimization/test/tests/executioners/steady_and_adjoint/multi_variable.i)
(modules/optimization/test/tests/executioners/steady_and_adjoint/self_adjoint.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/forward_and_adjoint.i)
(modules/optimization/test/tests/misc/scaling_test/scaling_test.i)
(modules/optimization/test/tests/executioners/steady_and_adjoint/nonhomogeneous_bc.i)
(modules/optimization/test/tests/executioners/steady_and_adjoint/nonlinear_diffusion.i)
(modules/optimization/test/tests/optimizationreporter/bimaterial/model_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/mesh_source/forward_and_adjoint.i)
(modules/optimization/test/tests/executioners/steady_and_adjoint/array_variable.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/forward_and_adjoint_transfer_data.i)
(modules/optimization/test/tests/executioners/constrained/inequality/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/nonlinear_material/forward_and_adjoint.i)
(modules/optimization/examples/materialFrequency/wave1D/model_grad.i)
(modules/optimization/test/tests/optimizationreporter/point_loads/forward_and_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/forward_and_adjoint.i)

(modules/optimization/test/tests/executioners/steady_and_adjoint/self_adjoint.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

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

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/self_adjoint.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

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

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/multi_variable.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [v]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
  [v_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [uv]
    type = CoupledForce
    variable = u
    v = v
    coef = 10
  []
  [vu]
    type = CoupledForce
    variable = v
    v = u
    coef = 1
  []
  [src_u]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_u_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 0
  []
  [src_v_adjoint]
    type = BodyForce
    variable = v_adjoint
    value = 1
  []
[]

[BCs]
  [dirichlet_u]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 0
  []
  [dirichlet_v]
    type = DirichletBC
    variable = v
    boundary = 'top right'
    value = 0
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/array_variable.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
    components = 2
  []
  [u_adjoint]
    components = 2
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = D
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = A
  []
  [src_u]
    type = ArrayBodyForce
    variable = u
    function = '1 0'
  []
  [src_adjoint]
    type = ArrayBodyForce
    variable = u_adjoint
    function = '0 1'
  []
[]

[Materials]
  [diffc]
    type = GenericConstantArray
    prop_name = 'D'
    prop_value = '1 1'
  []
  [coeff]
    type = GenericConstant2DArray
    prop_name = 'A'
    prop_value = '0 -10; -1 0'
  []
[]

[BCs]
  [dirichlet]
    type = ArrayDirichletBC
    variable = u
    boundary = 'top right'
    values = '0 0'
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/nonhomogeneous_bc.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 1
  []
  [neumann]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/nonlinear_diffusion.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = ADMatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = ADBodyForce
    variable = u
    value = 1
  []

  [src_adjoint]
    type = ADBodyForce
    variable = u_adjoint
    value = 1
  []
[]

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

[Materials]
  [diffc]
    type = ADParsedMaterial
    property_name = D
    expression = '0.1 + 5 * u'
    coupled_variables = 'u'
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
  []
  [u_adjoint_avg]
    type = ElementAverageValue
    variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
  [inner_product]
    type = VariableInnerProduct
    variable = u
    second_variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/nonhomogeneous_bc.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 1
  []
  [neumann]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
[]

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

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

[Outputs]
  exodus = true
[]

(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/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/nonlinear_material/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'heat_source'
  num_values = '1'
  initial_condition = '0'
  lower_bounds = '0.1'
  upper_bounds = '10000'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
                          0.8 0.6 0
                          0.2 1.4 0
                          0.8 1.8 0'
    measurement_values = '1.98404 1.91076 1.56488 1.23863'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol'
  petsc_options_value = ' 1e-5'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/heat_source'
    to_reporters = 'measurement_locations/measurement_xcoord
                    measurement_locations/measurement_ycoord
                    measurement_locations/measurement_zcoord
                    measurement_locations/measurement_time
                    measurement_locations/measurement_values
                    params/heat_source'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measurement_locations/objective_value
                      gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_heat_source'
  []
[]

[Outputs]
  csv = true
[]

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 1
    ymax = 1.4
  []
[]

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

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

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

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = temperature
    x_coord_name = 'point_source/x'
    y_coord_name = 'point_source/y'
    z_coord_name = 'point_source/z'
    value_name = 'point_source/value'
  []
  [misfit]
    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
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 300
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 300
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 300
  []
[]

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [gradient]
    type = PointValueSampler
    points = '0.2 0.2 0
              0.7 0.56 0
              0.4 1 0'
    variable = temperature_adjoint
    sort_by = id
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
    outputs = none
  []
  [point_source]
    type = ConstantReporter
    real_vector_names = 'x y z value'
    real_vector_values = '0.2 0.7 0.4;
                          0.2 0.56 1;
                          0 0 0;
                          -1000 120 500'
  []
[]

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

(modules/optimization/test/tests/executioners/steady_and_adjoint/multi_variable.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [v]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
  [v_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [uv]
    type = CoupledForce
    variable = u
    v = v
    coef = 10
  []
  [vu]
    type = CoupledForce
    variable = v
    v = u
    coef = 1
  []
  [src_u]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_u_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 0
  []
  [src_v_adjoint]
    type = BodyForce
    variable = v_adjoint
    value = 1
  []
[]

[BCs]
  [dirichlet_u]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 0
  []
  [dirichlet_v]
    type = DirichletBC
    variable = v
    boundary = 'top right'
    value = 0
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/self_adjoint.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

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

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

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

[Outputs]
  exodus = true
[]

(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/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/executioners/steady_and_adjoint/nonhomogeneous_bc.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 10
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 1
  []
  [neumann]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/nonlinear_diffusion.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = ADMatDiffusion
    variable = u
    diffusivity = D
  []
  [src]
    type = ADBodyForce
    variable = u
    value = 1
  []

  [src_adjoint]
    type = ADBodyForce
    variable = u_adjoint
    value = 1
  []
[]

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

[Materials]
  [diffc]
    type = ADParsedMaterial
    property_name = D
    expression = '0.1 + 5 * u'
    coupled_variables = 'u'
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
  []
  [u_adjoint_avg]
    type = ElementAverageValue
    variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
  [inner_product]
    type = VariableInnerProduct
    variable = u
    second_variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

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

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

[Outputs]
  exodus = true
[]

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

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

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

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

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

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

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

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

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

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

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

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

[Outputs]
  console = false
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/forward_and_adjoint.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 1
    ymax = 1.4
  []
[]

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

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

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

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = temperature
    x_coord_name = 'point_source/x'
    y_coord_name = 'point_source/y'
    z_coord_name = 'point_source/z'
    value_name = 'point_source/value'
  []
  [misfit]
    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
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 300
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 300
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 300
  []
[]

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [gradient]
    type = PointValueSampler
    points = '0.2 0.2 0
              0.7 0.56 0
              0.4 1 0'
    variable = temperature_adjoint
    sort_by = id
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    measurement_points = '0.5 0.28 0
    0.5 0.6 0
    0.5 0.8 0
    0.5 1.1 0'
    measurement_values = '293 304 315 320'
    objective_name = misfit_norm
  []
  [point_source]
    type = ConstantReporter
    real_vector_names = 'x y z value'
    real_vector_values = '0.2 0.7 0.4;
                          0.2 0.56 1;
                          0 0 0;
                          -1000 120 500'
  []
[]

[Outputs]
  console = false
[]

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

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

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

[Variables]
  [u]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [src]
    type = BodyForce
    variable = u
    function = src_func
  []
[]

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

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = u_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
  []
[]

[Functions]
  [src_func]
    type = ParameterMeshFunction
    exodus_mesh = parameter_mesh_in.e
    parameter_name = src_rep/vals
  []
[]

[Reporters]
  [src_rep]
    type = ConstantReporter
    real_vector_names = 'vals'
    real_vector_values = '1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0'
  []
  [measure_data]
    type = OptimizationData
    variable = u
    objective_name = objective_value
    outputs = none
  []
[]

[VectorPostprocessors]
  [gradient_vpp]
    type = ElementOptimizationSourceFunctionInnerProduct
    variable = u_adjoint
    function = src_func
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

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

[AuxVariables]
  [source]
  []
[]

[AuxKernels]
  [source_aux]
    type = FunctionAux
    variable = source
    function = src_func
  []
[]

[Outputs]
  exodus = true
  console = true
  execute_on = timestep_end
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/array_variable.i)

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

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
    components = 2
  []
  [u_adjoint]
    components = 2
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = D
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = A
  []
  [src_u]
    type = ArrayBodyForce
    variable = u
    function = '1 0'
  []
  [src_adjoint]
    type = ArrayBodyForce
    variable = u_adjoint
    function = '0 1'
  []
[]

[Materials]
  [diffc]
    type = GenericConstantArray
    prop_name = 'D'
    prop_value = '1 1'
  []
  [coeff]
    type = GenericConstant2DArray
    prop_name = 'A'
    prop_value = '0 -10; -1 0'
  []
[]

[BCs]
  [dirichlet]
    type = ArrayDirichletBC
    variable = u
    boundary = 'top right'
    values = '0 0'
  []
[]

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

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

[Outputs]
  exodus = true
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/forward_and_adjoint_transfer_data.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 1
    ymax = 1.4
  []
[]

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

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

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

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = temperature
    x_coord_name = 'point_source/x'
    y_coord_name = 'point_source/y'
    z_coord_name = 'point_source/z'
    value_name = 'point_source/value'
  []
  [misfit]
    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
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 300
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 300
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 300
  []
[]

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [gradient]
    type = PointValueSampler
    points = '0.2 0.2 0
              0.7 0.56 0
              0.4 1 0'
    variable = temperature_adjoint
    sort_by = id
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
    objective_name = misfit_norm
  []
  [point_source]
    type = ConstantReporter
    real_vector_names = 'x y z value'
    real_vector_values = '0.2 0.7 0.4;
                          0.2 0.56 1;
                          0 0 0;
                          -1000 120 500'
  []
[]

[Outputs]
  console = false
[]

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

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

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_forced_its = 1
  line_search = none
  nl_abs_tol = 1e-8
[]

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

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

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

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

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

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

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

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

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

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

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

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 1
    ymax = 1.4
  []
[]

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

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

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

[DiracKernels]
  [pt]
    type = ReporterPointSource
    variable = temperature
    x_coord_name = 'point_source/x'
    y_coord_name = 'point_source/y'
    z_coord_name = 'point_source/z'
    value_name = 'point_source/value'
  []
  [misfit]
    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
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 300
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  []
  [bottom]
    type = DirichletBC
    variable = temperature
    boundary = bottom
    value = 300
  []
  [top]
    type = DirichletBC
    variable = temperature
    boundary = top
    value = 300
  []
[]

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

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [gradient]
    type = PointValueSampler
    points = '0.2 0.2 0
              0.7 0.56 0
              0.4 1 0'
    variable = temperature_adjoint
    sort_by = id
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    objective_name = objective_value
    variable = temperature
  []
  [point_source]
    type = ConstantReporter
    real_vector_names = 'x y z value'
    real_vector_values = '0.2 0.7 0.4;
                          0.2 0.56 1;
                          0 0 0;
                          -1000 120 500'
  []
[]

[Outputs]
  console = false
[]

(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
[]

Overview
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Input Parameters
Input Files