AD material update and example

examples/ptr_inversion/material_obj/forward_and_adjoint.i

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+[Mesh]
+  [generated]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = 25
+    ny = 25
+    ymin = 0
+    xmin = 0
+    xmax = 10
+    ymax = 10
+  []
+  # coord_type = RZ
+[]
+
+[Problem]
+  nl_sys_names = 'nl0 adjoint'
+  kernel_coverage_check = FALSE
+[]
+
+[Variables]
+  [T_real]
+    initial_condition = 1e-8
+  []
+  [T_imag]
+    initial_condition = 1e-8
+  []
+  [T_real_adj]
+    initial_condition = 1e-8
+    solver_sys = adjoint
+  []
+  [T_imag_adj]
+    initial_condition = 1e-8
+    solver_sys = adjoint
+  []
+[]
+
+[Kernels]
+  [heat_conduction_real]
+    type = ADMatDiffusion
+    variable = T_real
+    diffusivity = k
+  []
+  [02596*]
+    type = MatCoupledForce
+    variable = T_real
+    v = T_imag
+    material_properties = 'force_mat'
+  []
+
+  [heat_conduction_imag]
+    type = ADMatDiffusion
+    variable = T_imag
+    diffusivity = k
+  []
+  [heat_source_imag]
+    type = MatCoupledForce
+    variable = T_imag
+    v = T_real
+    material_properties = 'force_mat'
+    coef = -1
+  []
+  [adj_source_real]
+    type = CoupledForce
+    variable = T_real_adj
+    v = obj_misfit_Treal_var
+  []
+  [adj_source_imag]
+    type = CoupledForce
+    variable = T_imag_adj
+    v = obj_misfit_Timag_var
+  []
+[]
+
+[Materials]
+  [k_mat]
+    type = ADGenericFunctionMaterial
+    prop_names = 'k'
+    prop_values = 'kappa_func'
+  []
+  [mats]
+    type = GenericConstantMaterial
+    prop_names = 'rho omega cp '
+    prop_values = '1.0 1.0 1.0 '
+  []
+  [force_mat]
+    type = ParsedMaterial
+    property_name = force_mat
+    expression = 'rho * omega * cp'
+    material_property_names = 'rho omega cp'
+  []
+  [phase]
+    type = ADParsedMaterial
+    coupled_variables = 'T_real T_imag'
+    expression = 'atan2(T_imag, T_real)'
+    property_name = phase
+    # outputs = exodus
+  []
+  [beam]
+    type = ADMaterialReporterOffsetFunctionMaterial
+    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/measurement_values
+    sim_material = phase
+    function = gauss
+    property_name = 'obj_misfit'
+    # outputs = exodus
+  []
+[]
+
+[Functions]
+  [gauss]
+    type = ParsedFunction
+    expression = 'exp(-2.0 *(x^2 + y^2 + z^2)/(beam_radii^2))'
+    symbol_names = 'beam_radii'
+    symbol_values = '0.1'
+  []
+  [kappa_func]
+    type = ParsedOptimizationFunction
+    expression = 'k '
+    param_symbol_names = 'k '
+    param_vector_name = 'params/k'
+  []
+[]
+
+[BCs]
+  [real_top]
+    type = FunctionNeumannBC
+    variable = T_real
+    boundary = top
+    function = 'exp((-2.0 *(x)^2)/0.1)'
+  []
+[]
+
+[AuxVariables]
+  [obj_misfit_Treal_var]
+    family = L2_LAGRANGE
+  []
+  [obj_misfit_Timag_var]
+    family = L2_LAGRANGE
+  []
+  [phase]
+  []
+  [adj_phase]
+  []
+[]
+[AuxKernels]
+  [obj_mis_real]
+    # This value needs to be saved for the adjoint system. Material system does
+    # not perserve ad info from one nl system to another
+    type = ADCoupledVarMaterialDerivativeAux
+    variable = obj_misfit_Treal_var
+    ad_prop_name = obj_misfit
+    coupled_var = T_real
+    execute_on = 'TIMESTEP_END'
+  []
+  [obj_mis_imag]
+    type = ADCoupledVarMaterialDerivativeAux
+    variable = obj_misfit_Timag_var
+    ad_prop_name = obj_misfit
+    coupled_var = T_imag
+    execute_on = 'TIMESTEP_END'
+  []
+  [phase]
+    type = ParsedAux
+    variable = phase
+    coupled_variables = 'T_imag T_real'
+    expression = 'atan2(T_imag, T_real)'
+    execute_on = 'TIMESTEP_END'
+  []
+
+  [adj]
+    type = ParsedAux
+    variable = adj_phase
+    coupled_variables = 'T_imag_adj T_real_adj'
+    expression = 'atan2(T_imag_adj, T_real_adj)'
+    execute_on = 'ADJOINT_TIMESTEP_END'
+  []
+[]
+
+[Postprocessors]
+  [objective]
+    type = ADElementIntegralMaterialProperty
+    mat_prop = obj_misfit
+    execute_on = 'TIMESTEP_END'
+  []
+[]
+[Reporters]
+  [measure_data]
+    type = OptimizationData
+    measurement_values = '-0.663 -2.86'
+    measurement_points = '0.55 10 0
+                          3.55 10 0'
+  []
+  [params]
+    type = ConstantReporter
+    real_vector_names = 'k'
+    real_vector_values = '2' # Dummy value
+  []
+  [gradient]
+    type = ParsedVectorReporter
+    name = inner
+    reporter_names = 'gradient_real/inner_product gradient_imag/inner_product'
+    reporter_symbols = 'real imag'
+    expression = 'real+imag'
+    execute_on = ADJOINT_TIMESTEP_END
+  []
+[]
+
+[VectorPostprocessors]
+  [gradient_real]
+    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
+    variable = T_real_adj
+    forward_variable = T_real
+    function = kappa_func
+    # boundary = top
+    execution_order_group = -1
+    execute_on = ADJOINT_TIMESTEP_END
+  []
+  [gradient_imag]
+    type = ElementOptimizationDiffusionCoefFunctionInnerProduct
+    variable = T_imag_adj
+    forward_variable = T_imag
+    function = kappa_func
+    # boundary = top
+    execution_order_group = -1
+    execute_on = ADJOINT_TIMESTEP_END
+  []
+
+[]
+
+[Executioner]
+  type = SteadyAndAdjoint
+  forward_system = nl0
+  adjoint_system = adjoint
+  nl_rel_tol = 1e-12
+  nl_abs_tol = 1e-10
+  automatic_scaling = true
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'lu'
+  verbose = true
+[]
+

examples/ptr_inversion/material_obj/main.i

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+[Optimization]
+[]
+
+[OptimizationReporter]
+  type = GeneralOptimization
+  objective_name = objective_value
+  parameter_names = 'parameter_results'
+  num_values = '1'
+  # Better to have larger initial conditon than smaller. Problem can have
+  # multiple solutions all on the smaller side.
+  initial_condition = '1.5'
+  lower_bounds = '0.0001'
+[]
+
+[Executioner]
+  type = Optimize
+  tao_solver = taobqnls
+  petsc_options_iname = '-tao_gatol -tao_max_it  -tao_ls_type'
+  petsc_options_value = '1e-6 1000 armijo'
+  verbose = true
+  output_optimization_iterations = true
+[]
+
+[MultiApps]
+  [forward]
+    type = FullSolveMultiApp
+    input_files = forward_and_adjoint.i
+    execute_on = "FORWARD"
+  []
+[]
+
+[Transfers]
+  # FORWARD transfers
+  [toForward_measument]
+    type = MultiAppReporterTransfer
+    to_multi_app = forward
+    from_reporters = 'OptimizationReporter/parameter_results'
+    to_reporters = 'params/k'
+  []
+  [fromForward]
+    type = MultiAppReporterTransfer
+    from_multi_app = forward
+    from_reporters = 'objective/value
+                     gradient/inner'
+    to_reporters = 'OptimizationReporter/objective_value
+                    OptimizationReporter/grad_parameter_results'
+  []
+[]
+
+[Outputs]
+  [out]
+    execute_system_information_on = NONE
+    type = JSON
+    execute_on = 'FORWARD FINAL'
+  []
+[]

examples/ptr_inversion/material_obj/tests

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+[Tests]
+  issues = '#97'
+  design = 'ADCoupledVarMaterialDerivativeAux.md'
+  [grad]
+    requirement = "The system shall be able to compute an compute gradient information automatically using AD materials."
+    type = JSONDiff
+    rel_err = 1e-5
+    abs_zero = 1.0e-6
+    input = main.i
+    jsondiff = main_out.json
+    max_threads = 1
+    # steady solve
+    recover = false
+  []
+[]

include/materials/MaterialReporterOffsetFunctionMaterial.h

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+#pragma once
+
+#include "MooseTypes.h"
+#include "ReporterOffsetFunctionMaterial.h"
+#include "Function.h"
+
+template <bool>
+class MaterialReporterOffsetFunctionMaterialTempl;
+typedef MaterialReporterOffsetFunctionMaterialTempl<false> MaterialReporterOffsetFunctionMaterial;
+typedef MaterialReporterOffsetFunctionMaterialTempl<true> ADMaterialReporterOffsetFunctionMaterial;
+
+/**
+ * This class creates a misfit and misfit gradient material that can be used for
+ * optimizing measurements weighted by functions.
+ */
+template <bool is_ad>
+class MaterialReporterOffsetFunctionMaterialTempl
+  : public ReporterOffsetFunctionMaterialTempl<is_ad>
+{
+public:
+  static InputParameters validParams();
+
+  MaterialReporterOffsetFunctionMaterialTempl<is_ad>(const InputParameters & parameters);
+
+protected:
+  virtual void computeQpProperties() override;
+
+  /// Coupled Material to scale by
+  const GenericMaterialProperty<Real, is_ad> & _coupled_material;
+
+  /// Gradient of misfit with respect to the coupled_material
+  GenericMaterialProperty<Real, is_ad> & _mat_prop_gradient;
+
+  /// values at each xyz coordinate
+  const std::vector<Real> & _measurement_values;
+
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_prop_name;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_qp;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_material;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_points;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_read_in_points;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_coordx;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_coordy;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::_coordz;
+  using ReporterOffsetFunctionMaterialTempl<is_ad>::computeOffsetFunction;
+};