bimaterial inversion using adjoint based gradient closes idaholab#30

modules/optimization/test/tests/optimizationreporter/objective_gradient_minimize/bimaterial/grad.i

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+[Mesh]
+  [gmg]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = 16
+    ny = 16
+    xmin = -4
+    xmax = 4
+    ymin = -4
+    ymax = 4
+  []
+  [bimaterial]
+    type = SubdomainBoundingBoxGenerator
+    input = gmg
+    block_id = 1
+    bottom_left = '-100 -100 -100'
+    top_right = '100 0 100'
+  []
+  [name_blocks]
+    type = RenameBlockGenerator
+    input = bimaterial
+    old_block = '0 1'
+     new_block = 'top bottom'
+  []
+[]
+
+[Variables]
+  [temperature]
+  []
+[]
+
+[Kernels]
+  [conduction]
+    type = MatDiffusion
+    diffusivity = diffusivity
+    variable = temperature
+  []
+[]
+
+
+[Reporters]
+  [misfit]
+    type=OptimizationData
+  []
+[]
+
+[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
+  []
+[]
+
+[BCs]
+  [bottom]
+    type = DirichletBC
+    variable = temperature
+    boundary = bottom
+    value = 0
+  []
+[]
+
+[AuxVariables]
+  [forwardAdjoint]
+  []
+  [temperature_forward]
+  []
+  [grad_Tx]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [grad_Ty]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [grad_Tz]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [grad_Tfx]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [grad_Tfy]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [grad_Tfz]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+  [gradient]
+    order = CONSTANT
+    family = MONOMIAL
+  []
+[]
+
+[AuxKernels]
+  [grad_Tx]
+    type = VariableGradientComponent
+    component = x
+    variable = grad_Tx
+    gradient_variable = temperature
+  []
+  [grad_Ty]
+    type = VariableGradientComponent
+    component = y
+    variable = grad_Ty
+    gradient_variable = temperature
+  []
+  [grad_Tz]
+    type = VariableGradientComponent
+    component = z
+    variable = grad_Tz
+    gradient_variable = temperature
+  []
+  [grad_Tfx]
+    type = VariableGradientComponent
+    component = x
+    variable = grad_Tfx
+    gradient_variable = temperature_forward
+  []
+  [grad_Tfy]
+    type = VariableGradientComponent
+    component = y
+    variable = grad_Tfy
+    gradient_variable = temperature_forward
+  []
+  [grad_Tfz]
+    type = VariableGradientComponent
+    component = z
+    variable = grad_Tfz
+    gradient_variable = temperature_forward
+  []
+  [gradient]
+    type = ParsedAux
+    variable = gradient
+    args = 'grad_Tx grad_Ty grad_Tz grad_Tfx grad_Tfy grad_Tfz'
+    function = '-grad_Tx*grad_Tfx-grad_Ty*grad_Tfy-grad_Tz*grad_Tfz'#we need to include the material derivative, which can be captured when computing the flux based on the derivative of the material.
+  []
+  [forwardAdjoint] # I am not sure why do we need this?
+    type = ParsedAux
+    variable = forwardAdjoint
+    args = 'temperature_forward temperature'
+    function = 'temperature_forward*temperature'
+  []
+[]
+
+[Functions]
+  [diffusivity_top_function]
+    type = ParsedFunction
+    value = alpha
+    vars = alpha
+    vals = d_top
+  []
+  [diffusivity_bottom_function]
+    type = ParsedFunction
+    value = alpha
+    vars = alpha
+    vals = d_bot
+  []
+[]
+
+[Materials] #same material as what was used in the forward model
+  [mat_top]
+    type = GenericFunctionMaterial
+    block = top
+    prop_names = diffusivity
+    prop_values = diffusivity_top_function
+  []
+  [mat_bottom]
+    type = GenericFunctionMaterial
+    block = bottom
+    prop_names = diffusivity
+    prop_values = diffusivity_bottom_function
+  []
+[]
+
+[Postprocessors]
+  [d_bot]
+    type = VectorPostprocessorComponent
+    index = 0
+    vectorpostprocessor = vector_pp
+    vector_name = diffusivity_values
+    execute_on = 'linear'
+  []
+  [d_top]
+    type = VectorPostprocessorComponent
+    index = 1
+    vectorpostprocessor = vector_pp
+    vector_name = diffusivity_values
+    execute_on = 'linear'
+  []
+  ############
+  # we need to combine the two in one vector.
+  [grad_bottom] #compute the integral of the gradient variable on the bottom block (first parameter)
+    type = ElementIntegralVariablePostprocessor
+    variable = gradient
+    execute_on = 'final'
+    block=bottom
+    outputs=grad_bottom
+  []
+  [grad_top] #compute the integral of the gradient variable on the bottom block (second parameter)
+    type = ElementIntegralVariablePostprocessor
+    variable = gradient
+    execute_on = 'final'
+    block=top
+    outputs=grad_top
+  []
+  ############
+[]
+
+[VectorPostprocessors]
+  [vector_pp]
+    type = ConstantVectorPostprocessor
+    vector_names = diffusivity_values
+    value = '1.0 10.0' #we need to set initial values (any values)- these will be over-written
+  []
+  [gradvec]
+    type = VectorOfPostprocessors
+    postprocessors = 'grad_bottom grad_top'
+    execute_on = 'final'
+  []
+[]
+
+[Executioner]
+  type = Steady
+  solve_type = NEWTON
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'lu'
+  nl_forced_iters = 1
+  line_search=none
+  nl_abs_tol=1e-8
+[]
+
+[Outputs]
+  console = false
+  file_base = 'adjoint'
+[]

modules/optimization/test/tests/optimizationreporter/objective_gradient_minimize/bimaterial/main.i

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+# This main.i file runs the subapps model.i and grad.i, using an OptimizeFullSolveMultiApp
+# The purpose of main.i is to find the two diffusivity_values
+# (one in the bottom material of model.i, and one in the top material of model.i)
+# such that the misfit between experimental observations (defined in model.i) and MOOSE predictions is minimised.
+# The adjoint computed in grad.i is used to compute the gradient for the gradient based LMVM solver in TAO
+# PETSc-TAO optimisation is used to perform this inversion
+#
+[StochasticTools]
+[]
+[Mesh]
+  [gmg]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = 16
+    ny = 16
+    xmin = -4
+    xmax = 4
+    ymin = -4
+    ymax = 4
+  []
+  [bimaterial]
+    type = SubdomainBoundingBoxGenerator
+    input = gmg
+    block_id = 1
+    bottom_left = '-100 -100 -100'
+    top_right = '100 0 100'
+  []
+  [name_blocks]
+    type = RenameBlockGenerator
+    input = bimaterial
+    old_block = '0 1'
+     new_block = 'top bottom'
+  []
+[]
+
+[OptimizationReporter]
+  type = ObjectiveGradientMinimize
+  parameter_names = diffusivity_values
+  num_values = 2 # diffusivity in the bottom material and in the top material of model.i
+  initial_condition = '3 4' # the expected result is about '1 10' so this initial condition is not too bad
+  lower_bounds = '1 1'
+  upper_bounds = '20 20'
+  measurement_file = 'synthetic_data.csv'
+  file_value = 'temperature'
+[]
+
+[Executioner]
+   # type = Optimize
+   # tao_solver = taoblmvm
+   # petsc_options_iname = '-tao_fd_gradient -tao_gatol'
+   # petsc_options_value = ' true            0.001'
+   type = Optimize
+   tao_solver = taoblmvm
+   petsc_options_iname='-tao_gatol'
+   petsc_options_value='1e-3'
+   ## THESE OPTIONS ARE FOR TESTING THE ADJOINT GRADIENT
+   # petsc_options_iname='-tao_max_it -tao_fd_test -tao_test_gradient -tao_fd_gradient -tao_fd_delta -tao_gatol'
+   # petsc_options_value='1 true true false 1e-8 0.1'
+   # petsc_options = '-tao_test_gradient_view'
+   # verbose = true
+[]
+[AuxVariables]
+  [temperature_forward]
+  []
+[]
+[MultiApps]
+  [forward]
+    type = OptimizeFullSolveMultiApp
+    input_files = model.i
+    execute_on = "FORWARD"
+    clone_parent_mesh = true
+    ignore_solve_not_converge = false
+  []
+  [adjoint]
+    type = OptimizeFullSolveMultiApp
+    input_files = grad.i #write this input file to compute the adjoint solution and the gradient
+    execute_on = "ADJOINT"
+    clone_parent_mesh = true
+    ignore_solve_not_converge = false
+  []
+[]
+
+[Transfers]
+  [diffusivity_to_forward] #update the model with the new parameters
+    type = MultiAppReporterTransfer
+    to_multi_app = forward
+    from_reporters = 'OptimizationReporter/diffusivity_values'
+    to_reporters = 'vector_pp/diffusivity_values'
+  []
+  [toForward_measument] #pass the coordinates where we knew the measurements to the forward model to do the extraction of the simulation data at the location of the measurements to compute the misfit
+    type = MultiAppReporterTransfer
+    to_multi_app = forward
+    from_reporters = 'OptimizationReporter/measurement_xcoord OptimizationReporter/measurement_ycoord OptimizationReporter/measurement_zcoord'
+    to_reporters = 'measure_data/measurement_xcoord measure_data/measurement_ycoord measure_data/measurement_zcoord'
+  []
+  [from_forward] #get the simulation values
+    type = MultiAppReporterTransfer
+    from_multi_app = forward
+    from_reporters = 'data_pt/temperature'
+    to_reporters = 'OptimizationReporter/simulation_values'
+  []
+  #############
+  #copy the temprature variable - we will need this for the compuation of the gradient
+  [fromforwardMesh]
+    type = MultiAppCopyTransfer
+    from_multi_app = forward
+    source_variable = 'temperature'
+    variable = 'temperature_forward'
+  []
+  [toAdjointMesh]
+    type = MultiAppCopyTransfer
+    to_multi_app = adjoint
+    source_variable = 'temperature_forward'
+    variable = 'temperature_forward'
+  []
+  #############
+  [diffusivity_to_adjoint] #update the adjoint with the new parameters
+    type = MultiAppReporterTransfer
+    to_multi_app = adjoint
+    from_reporters = 'OptimizationReporter/diffusivity_values'
+    to_reporters = 'vector_pp/diffusivity_values'
+  []
+  [toAdjoint]#pas the misfit to the adjoint
+    type = MultiAppReporterTransfer
+    to_multi_app = adjoint
+    from_reporters = 'OptimizationReporter/measurement_xcoord OptimizationReporter/measurement_ycoord OptimizationReporter/measurement_zcoord OptimizationReporter/misfit_values'
+    to_reporters = 'misfit/measurement_xcoord misfit/measurement_ycoord misfit/measurement_zcoord misfit/misfit_values'
+  []
+  [fromadjoint]
+    type = MultiAppReporterTransfer
+    from_multi_app = adjoint
+    from_reporters = 'gradvec/gradvec'
+    to_reporters = 'OptimizationReporter/adjoint'
+  []
+[]
+
+[Outputs]
+  csv=true
+[]