MisfitReporterOffsetFunctionMaterial

Computes the misfit and misfit gradient materials for inverse optimizations problems.

Overview

The MisfitReporterOffsetFunctionMaterial material computes the misfit and its gradient with respect to a simulation variable , using a user-defined offset function to weight the contribution of measurement points. This material is particularly useful for inverse optimization problems where you want to match simulation results to experimental or observed data. The material name given to the misfit is "property_name" and the misfit gradient material uses the naming convention "property_name"+_gradient.

Measurement data:

Measurement values are provide by the reporter "measurement_value_name" and the corresponding measurement locations are given by a reporter containing either a vector of points "point_name" or three separate reporters each containing the x, y and z coordinates respectively of the points using "x_coord_name", "y_coord_name", and "z_coord_name".

Measurement values: $var element = document.getElementById("moose-equation-e081ff36-e2aa-4bc8-ae50-250b0fdfebca");katex.render("\\mathbf{u}_m = \\{u_{m,1}, u_{m,2}, \\ldots, u_{m,n}\\}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Measurement locations: $var element = document.getElementById("moose-equation-c2c2d594-bda5-4f85-b724-da09e9a8742d");katex.render("\\mathbf{p}_m = \\{\\mathbf{p}_{m,1}, \\mathbf{p}_{m,2}, \\ldots, \\mathbf{p}_{m,n}\\}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-fc2929fe-1fa9-43f9-9ad6-76b6bdea2265");katex.render("\\mathbf{p}_{m,i} = (x_{m,i}, y_{m,i}, z_{m,i})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for 3D data
Simulation variable: $var element = document.getElementById("moose-equation-e61187d6-c9ff-47d2-aa18-6dc834efc10f");katex.render("u(\\mathbf{x})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Offset function: $var element = document.getElementById("moose-equation-f3fba0f7-0987-47ac-80da-0d9d764e1c00");katex.render("g(\\mathbf{p}, \\mathbf{x}; \\mathbf{\\theta})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-24b59dbd-33c6-4462-b33d-f1e1caf8c534");katex.render("\\mathbf{\\theta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the parameters defining the offset function
Simulation point: $var element = document.getElementById("moose-equation-a84cbe8b-4c86-40a0-924f-b1cd6756afb8");katex.render("\\mathbf{x}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Misfit and gradient calculation:

The misfit at a given simulation point $var element = document.getElementById("moose-equation-70afa36f-0159-485b-905c-8110c2296a78");katex.render("\\mathbf{x}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is calculated as:

$var element = document.getElementById("moose-equation-a72533e5-2b32-455f-b203-e551ae662b54");katex.render("m(\\mathbf{x}) = \\sum_{i=1}^{n} \\left( u_{m,i} g(\\mathbf{p}_{m,i}, \\mathbf{x}; \\mathbf{\\theta}) - u(\\mathbf{x}) g(\\mathbf{p}_{m,i}, \\mathbf{x}; \\mathbf{\\theta}) \\right)^2,", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

and the misfit_gradient with respect to the simulation variable $var element = document.getElementById("moose-equation-89e37373-9f58-42cd-8093-c8cfcc077d87");katex.render("u(\\mathbf{x})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is:

$var element = document.getElementById("moose-equation-319e152f-bb00-4ce7-8328-b73060c4a25f");katex.render("\\frac{\\partial m(\\mathbf{x})}{\\partial u(\\mathbf{x})} = -2 \\sum_{i=1}^{n} g(\\mathbf{p}_{m,i}, \\mathbf{x}; \\mathbf{\\theta}) \\left( u_{m,i} g(\\mathbf{p}_{m,i}, \\mathbf{x}; \\mathbf{\\theta}) - u(\\mathbf{x}) g(\\mathbf{p}_{m,i}, \\mathbf{x}; \\mathbf{\\theta}) \\right).", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

These equations represent the misfit value and its gradient computed by the MisfitReporterOffsetFunctionMaterial material at each quadrature point in the simulation. The misfit value quantifies the discrepancy between the measured data and the simulation variable, while the misfit gradient provides the sensitivity of the misfit with respect to changes in the simulation variable.

Example Input File Syntax

The following input file contains an example of how to use this material to define gaussian shaped measurement points in a heat source inversion problem where the misfit is used in the computation of the objective function and the misfit_gradient is used to compute the right hand side in the adjoint problem.

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [beam]
    type = MisfitReporterOffsetFunctionMaterial<<<{"description": "Computes the misfit and misfit gradient materials for inverse optimizations problems.", "href": "MisfitReporterOffsetFunctionMaterial.html"}>>>
    x_coord_name<<<{"description": "Reporter with x-coordinate data."}>>> = measure_data/measurement_xcoord
    y_coord_name<<<{"description": "Reporter with y-coordinate data."}>>> = measure_data/measurement_ycoord
    z_coord_name<<<{"description": "Reporter with z-coordinate data."}>>> = measure_data/measurement_zcoord
    measurement_value_name<<<{"description": "Reporter with measurement data."}>>> = measure_data/measurement_values
    forward_variable<<<{"description": "Variable that is being used for the forward simulation."}>>> = temperature
    property_name<<<{"description": "Material property base name"}>>> = 'obj_misfit'
    function<<<{"description": "The weighting function."}>>> = gauss
  []
[]

Syntax parameters and inputs

Input Parameters

forward_variableVariable that is being used for the forward simulation.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable that is being used for the forward simulation.
functionThe weighting function.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The weighting function.
measurement_value_nameReporter with measurement data.
C++ Type:ReporterName
Controllable:No
Description:Reporter with measurement data.
property_nameMaterial property base name
C++ Type:std::string
Controllable:No
Description:Material property base name

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

point_nameReporter with point data. /.
C++ Type:ReporterName
Controllable:No
Description:Reporter with point data. /.
x_coord_nameReporter with x-coordinate data.
C++ Type:ReporterName
Controllable:No
Description:Reporter with x-coordinate data.
y_coord_nameReporter with y-coordinate data.
C++ Type:ReporterName
Controllable:No
Description:Reporter with y-coordinate data.
z_coord_nameReporter with z-coordinate data.
C++ Type:ReporterName
Controllable:No
Description:Reporter with z-coordinate data.

Offset Locations For Function Evaluations Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(modules/optimization/test/tests/optimizationreporter/function_misfit/forward_and_adjoint_side.i)
(modules/optimization/test/tests/optimizationreporter/function_misfit/forward_and_adjoint.i)

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 15
    ny = 15
    xmin = 0
    ymin = 0
    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
  []
  # apply gradient material as a body force since the integral is over the whole domain
  [adj_source]
    type = MatBodyForce
    variable = temperature_adjoint
    material_property = obj_misfit_gradient
  []
[]

[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'
  []
[]

[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
  []
  # Create two materials.
  # 1. Material which the integral of is our objective
  # 2. dM/du material which is used for our adjoint problem
  [beam]
    type = MisfitReporterOffsetFunctionMaterial
    x_coord_name = measure_data/measurement_xcoord
    y_coord_name = measure_data/measurement_ycoord
    z_coord_name = measure_data/measurement_zcoord
    measurement_value_name = measure_data/measurement_values
    forward_variable = temperature
    property_name = 'obj_misfit'
    function = gauss
  []
[]

[Functions]
  [gauss]
    type = ParsedFunction
    expression = 'exp(-2.0 *(x^2 + y^2 + z^2)/(beam_radii^2))'
    symbol_names = 'beam_radii'
    symbol_values = '.025'
  []
[]

[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
  []
[]
[Postprocessors]
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = obj_misfit
    execute_on = 'ADJOINT_TIMESTEP_END TIMESTEP_END'
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    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/function_misfit/forward_and_adjoint_side.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 15
    ny = 15
    xmin = 0
    ymin = 0
    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'
  []
[]

[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
  []
  # apply gradient material as a side force since the objective integral is only
  # over this side
  [top]
    type = MatNeumannBC
    boundary = top
    boundary_material = obj_misfit_gradient
    variable = temperature_adjoint
    value = 1
  []
[]

[Materials]
  [steel]
    type = GenericConstantMaterial
    prop_names = thermal_conductivity
    prop_values = 5
  []
  # Create two materials.
  # 1. Material which the integral of is our objective
  # 2. dM/du material which is used for our adjoint problem
  [beam]
    type = MisfitReporterOffsetFunctionMaterial
    x_coord_name = measure_data/measurement_xcoord
    y_coord_name = measure_data/measurement_ycoord
    z_coord_name = measure_data/measurement_zcoord
    measurement_value_name = measure_data/measurement_values
    forward_variable = temperature
    property_name = obj_misfit
    function = gauss
  []
[]

[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
  []
[]
[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-12
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[VectorPostprocessors]
  [gradient]
    type = PointValueSampler
    points = '0.2 1.1 0
    0.7 1.1 0
    0.4 1.1 0'
    variable = temperature_adjoint
    sort_by = id
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Postprocessors]
  [objective]
    type = SideIntegralMaterialProperty
    boundary = top
    property = obj_misfit
    execute_on = 'TIMESTEP_END'
  []
  [largest_adjoint]
    type = NodalExtremeValue
    variable = temperature_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    variable = temperature
  []
  [point_source]
    type = ConstantReporter
    real_vector_names = 'x y z value'
    real_vector_values = '0.2 0.7 0.4;
                          1.1 1.1 1.1;
                          0 0 0;
                          -1000 120 500'
  []
[]

[Outputs]
  console = false
[]

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

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 15
    ny = 15
    xmin = 0
    ymin = 0
    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
  []
  # apply gradient material as a body force since the integral is over the whole domain
  [adj_source]
    type = MatBodyForce
    variable = temperature_adjoint
    material_property = obj_misfit_gradient
  []
[]

[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'
  []
[]

[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
  []
  # Create two materials.
  # 1. Material which the integral of is our objective
  # 2. dM/du material which is used for our adjoint problem
  [beam]
    type = MisfitReporterOffsetFunctionMaterial
    x_coord_name = measure_data/measurement_xcoord
    y_coord_name = measure_data/measurement_ycoord
    z_coord_name = measure_data/measurement_zcoord
    measurement_value_name = measure_data/measurement_values
    forward_variable = temperature
    property_name = 'obj_misfit'
    function = gauss
  []
[]

[Functions]
  [gauss]
    type = ParsedFunction
    expression = 'exp(-2.0 *(x^2 + y^2 + z^2)/(beam_radii^2))'
    symbol_names = 'beam_radii'
    symbol_values = '.025'
  []
[]

[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
  []
[]
[Postprocessors]
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = obj_misfit
    execute_on = 'ADJOINT_TIMESTEP_END TIMESTEP_END'
  []
[]

[Reporters]
  [measure_data]
    type = OptimizationData
    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
[]

Overview
Example Input File Syntax
Syntax parameters and inputs
Input Parameters
Input Files