[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Variables]
  [u]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [time]
    type = TimeDerivative
    variable = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 0.01
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Controls]
  [stochastic]
    type = SamplerReceiver
  []
[]

[Postprocessors]
  [left_bc]
    type = PointValue
    point = '0 0 0'
    variable = u
  []
  [right_bc]
    type = PointValue
    point = '1 0 0'
    variable = u
  []
  [avg]
    type = ElementAverageValue
    variable = u
    # execute_on = 'FINAL'
  []
  [objective]
    type = ParsedPostprocessor
    function = '-(avg - 0.2)^2'   # target = 0.5
    pp_names = 'avg'
    # execute_on = 'FINAL'
    execute_on = 'TIMESTEP_END'
  []
[]

[Outputs]
  csv = false
[]