SecantInversionControl

Adjusts a parameter postprocessor each fixed-point iteration using the secant method so that a sub-app output postprocessor matches a target function of time.

Overview

SecantInversionControl helps solve a scalar inverse problem inside a fixed-point (Picard) iteration: at each time step it adjusts a parameter p (held in a Receiver postprocessor and transferred to a sub-application) so that a sub-application output postprocessor matches a target Function of time.

Each fixed-point iteration, after the sub-application has solved with the current p and its output has been transferred back, this control performs a single secant (quasi-Newton) update:

var element = document.getElementById("moose-equation-1bb8a8e7-2147-43a4-8a01-d1f870ffb191");katex.render("p_{k+1} = p_k - (y_k - y_\\text{target}) \\frac{p_k - p_{k-1}}{y_k - y_{k-1}}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

On the first iteration of each fixed-point solve only one (p, y) pair is available, so the update is seeded by perturbing p by initial_delta. The outer iteration count, convergence test, and time-step cutting are owned by the Executioner and the Convergence system (typically a PostprocessorConvergence on the output residual), not by this control.

The optional converged_parameter_postprocessor receives the parameter value that produced the current output; at convergence it holds the inverse-problem solution.

Example Input Syntax

[Controls<<<{"href": "../../syntax/Controls/index.html"}>>>]
  [secant]
    type = SecantInversionControl<<<{"description": "Adjusts a parameter postprocessor each fixed-point iteration using the secant method so that a sub-app output postprocessor matches a target function of time.", "href": "SecantInversionControl.html"}>>>
    output_postprocessor<<<{"description": "Postprocessor holding the sub-app output to compare against the target."}>>> = output
    parameter_postprocessor<<<{"description": "Postprocessor (e.g. a Receiver) holding the parameter value; read and updated in place."}>>> = p
    residual_postprocessor<<<{"description": "Postprocessor (e.g. a Receiver) the control writes with the normalized convergence residual; point the fixed-point Convergence object at it with a tolerance of 1."}>>> = residual
    converged_parameter_postprocessor<<<{"description": "Optional postprocessor to which the parameter value that produced the current output is written each iteration; at convergence this holds the inverse-problem solution."}>>> = param_value
    target_function<<<{"description": "Function f(t) giving the target output value at each time step."}>>> = target_fn
    initial_delta<<<{"description": "Perturbation applied to the parameter on the first iteration of each fixed-point solve to seed the secant method."}>>> = 1e-3
  []
[]

[Convergence<<<{"href": "../../syntax/Convergence/index.html"}>>>]
  [inv_conv]
    type = PostprocessorConvergence<<<{"description": "Compares the absolute value of a post-processor to a tolerance.", "href": "../convergence/PostprocessorConvergence.html"}>>>
    postprocessor<<<{"description": "Post-processor to use for convergence criteria"}>>> = residual
    tolerance<<<{"description": "Tolerance to use for convergence criteria"}>>> = 1.0
    max_iterations<<<{"description": "Maximum number of iterations"}>>> = 50
  []
[]

Input Parameters

output_postprocessorPostprocessor holding the sub-app output to compare against the target.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor holding the sub-app output to compare against the target.
parameter_postprocessorPostprocessor (e.g. a Receiver) holding the parameter value; read and updated in place.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor (e.g. a Receiver) holding the parameter value; read and updated in place.
residual_postprocessorPostprocessor (e.g. a Receiver) the control writes with the normalized convergence residual; point the fixed-point Convergence object at it with a tolerance of 1.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor (e.g. a Receiver) the control writes with the normalized convergence residual; point the fixed-point Convergence object at it with a tolerance of 1.
target_functionFunction f(t) giving the target output value at each time step.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function f(t) giving the target output value at each time step.

Required Parameters

absolute_tolerance1e-08Absolute tolerance on |output - target|.
Default:1e-08
C++ Type:Real
Unit:(no unit assumed)
Range:absolute_tolerance>0
Controllable:No
Description:Absolute tolerance on |output - target|.
converged_parameter_postprocessorOptional postprocessor to which the parameter value that produced the current output is written each iteration; at convergence this holds the inverse-problem solution.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Optional postprocessor to which the parameter value that produced the current output is written each iteration; at convergence this holds the inverse-problem solution.
depends_onThe Controls that this control relies upon (i.e. must execute before this one)
C++ Type:std::vector<std::string>
Controllable:No
Description:The Controls that this control relies upon (i.e. must execute before this one)
execute_onTIMESTEP_BEGINThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_BEGIN
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM, PRE_MULTIAPP_SETUP
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
initial_delta0.001Perturbation applied to the parameter on the first iteration of each fixed-point solve to seed the secant method.
Default:0.001
C++ Type:Real
Unit:(no unit assumed)
Range:initial_delta>0
Controllable:No
Description:Perturbation applied to the parameter on the first iteration of each fixed-point solve to seed the secant method.
relative_tolerance1e-06Relative tolerance on |output - target|, taken relative to |target|.
Default:1e-06
C++ Type:Real
Unit:(no unit assumed)
Range:relative_tolerance>0
Controllable:No
Description:Relative tolerance on |output - target|, taken relative to |target|.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.
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

Advanced Parameters

Input Files

(modules/optimization/test/tests/controls/inverse_solve/secant.i)

(modules/optimization/test/tests/controls/inverse_solve/secant.i)

# Hand-written driver for SecantInversionControl.
#
# Finds param p(t) such that the forward output u(t) matches target f(t) = t^2.
# Analytic solution (dt = 1): p(t) = 2*t - 1  =>  u = 1, 4, 9, 16, 25 at t = 1..5.
# The converged parameter is published to `param_value` (1, 3, 5, 7, 9).
#
# The tests reuse this input with cli_args to reach the nonconverging cases: a one-iteration
# budget (error and accept-on-max), and the nonlinear forward model that secant cannot solve.

# Supplies the Mesh and a Problem that skips the nonlinear-system check, so this orchestrating
# main app needs no variables of its own.
[Optimization]
[]

[Functions]
  [target_fn]
    type = ParsedFunction
    expression = 't^2'
  []
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    input_files = forward_linear.i
    execute_on = TIMESTEP_BEGIN
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppPostprocessorTransfer
    to_multi_app = sub
    from_postprocessor = p
    to_postprocessor = param_pp
  []
  [from_sub]
    type = MultiAppPostprocessorTransfer
    from_multi_app = sub
    from_postprocessor = output_pp
    to_postprocessor = output
    reduction_type = average
  []
[]

[Postprocessors]
  # Working parameter guess: transferred to the sub, read and updated by the Control.
  [p]
    type = Receiver
    default = 1.0
    outputs = none
  []
  # Sub-app output, filled by the FROM transfer.
  [output]
    type = Receiver
    outputs = none
  []
  # Convergence residual, written (normalized) by the Control each iteration.
  [residual]
    type = Receiver
    default = 1e30
    outputs = none
  []
  # Published converged parameter (the inverse-problem solution). This is the CSV output.
  [param_value]
    type = Receiver
    default = 0.0
  []
[]

[Controls]
  [secant]
    type = SecantInversionControl
    output_postprocessor = output
    parameter_postprocessor = p
    residual_postprocessor = residual
    converged_parameter_postprocessor = param_value
    target_function = target_fn
    initial_delta = 1e-3
  []
[]

[Convergence]
  [inv_conv]
    type = PostprocessorConvergence
    postprocessor = residual
    tolerance = 1.0
    max_iterations = 50
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 1
  solve_type = NEWTON
  multiapp_fixed_point_convergence = inv_conv
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/controls/inverse_solve/secant.i)

# Hand-written driver for SecantInversionControl.
#
# Finds param p(t) such that the forward output u(t) matches target f(t) = t^2.
# Analytic solution (dt = 1): p(t) = 2*t - 1  =>  u = 1, 4, 9, 16, 25 at t = 1..5.
# The converged parameter is published to `param_value` (1, 3, 5, 7, 9).
#
# The tests reuse this input with cli_args to reach the nonconverging cases: a one-iteration
# budget (error and accept-on-max), and the nonlinear forward model that secant cannot solve.

# Supplies the Mesh and a Problem that skips the nonlinear-system check, so this orchestrating
# main app needs no variables of its own.
[Optimization]
[]

[Functions]
  [target_fn]
    type = ParsedFunction
    expression = 't^2'
  []
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    input_files = forward_linear.i
    execute_on = TIMESTEP_BEGIN
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppPostprocessorTransfer
    to_multi_app = sub
    from_postprocessor = p
    to_postprocessor = param_pp
  []
  [from_sub]
    type = MultiAppPostprocessorTransfer
    from_multi_app = sub
    from_postprocessor = output_pp
    to_postprocessor = output
    reduction_type = average
  []
[]

[Postprocessors]
  # Working parameter guess: transferred to the sub, read and updated by the Control.
  [p]
    type = Receiver
    default = 1.0
    outputs = none
  []
  # Sub-app output, filled by the FROM transfer.
  [output]
    type = Receiver
    outputs = none
  []
  # Convergence residual, written (normalized) by the Control each iteration.
  [residual]
    type = Receiver
    default = 1e30
    outputs = none
  []
  # Published converged parameter (the inverse-problem solution). This is the CSV output.
  [param_value]
    type = Receiver
    default = 0.0
  []
[]

[Controls]
  [secant]
    type = SecantInversionControl
    output_postprocessor = output
    parameter_postprocessor = p
    residual_postprocessor = residual
    converged_parameter_postprocessor = param_value
    target_function = target_fn
    initial_delta = 1e-3
  []
[]

[Convergence]
  [inv_conv]
    type = PostprocessorConvergence
    postprocessor = residual
    tolerance = 1.0
    max_iterations = 50
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 1
  solve_type = NEWTON
  multiapp_fixed_point_convergence = inv_conv
[]

[Outputs]
  csv = true
[]

Overview
Example Input Syntax
Input Parameters
Input Files