cashocs.space_mapping.optimal_control#

Space mapping for optimal control problems.

Classes

CoarseModel(state_forms, bcs_list, ...[, ...])

Coarse Model for space mapping optimal control.

FineModel()

Base class for the fine model in space mapping.

ParameterExtraction(coarse_model, ...[, ...])

Parameter extraction for optimal control problems.

SpaceMappingProblem(fine_model, ...[, ...])

Space mapping method for optimal control problems.
class cashocs.space_mapping.optimal_control.CoarseModel(state_forms, bcs_list, cost_functional_form, states, controls, adjoints, config=None, riesz_scalar_products=None, control_constraints=None, initial_guess=None, ksp_options=None, adjoint_ksp_options=None, gradient_ksp_options=None, desired_weights=None, control_bcs_list=None, preconditioner_forms=None, pre_callback=None, post_callback=None, linear_solver=None, adjoint_linear_solver=None, newton_linearizations=None)[source]#

Bases: object

Coarse Model for space mapping optimal control.

Initializes self.

Parameters:

  • state_forms (Union[List[ufl.Form], ufl.Form]) – The list of weak forms for the coare state problem

  • bcs_list (Union[fenics.DirichletBC, List[fenics.DirichletBC], List[List[fenics.DirichletBC]]]) – The list of boundary conditions for the coarse problem

  • cost_functional_form (Union[List[_typing.CostFunctional], _typing.CostFunctional]) – The cost functional for the coarse problem

  • states (Union[List[fenics.Function], fenics.Function]) – The state variables for the coarse problem

  • controls (Union[List[fenics.Function], fenics.Function]) – The control variables for the coarse problem

  • adjoints (Union[List[fenics.Function], fenics.Function]) – The adjoint variables for the coarse problem

  • config (Optional[io.Config]) – config: The config file for the problem, generated via cashocs.load_config(). Alternatively, this can also be None, in which case the default configurations are used, except for the optimization algorithm. This has then to be specified in the solve method. The default is None.

  • riesz_scalar_products (Optional[Union[ufl.Form, List[ufl.Form]]]) – The scalar products for the coarse problem

  • control_constraints (Optional[List[List[Union[float, fenics.Function]]]]) – The box constraints for the problem

  • initial_guess (Optional[List[fenics.Function]]) – The initial guess for solving a nonlinear state equation

  • ksp_options (Optional[Union[_typing.KspOption, List[_typing.KspOption]]]) – The list of PETSc options for the state equations.

  • adjoint_ksp_options (Optional[Union[_typing.KspOption, List[_typing.KspOption]]]) – The list of PETSc options for the adjoint equations.

  • gradient_ksp_options (Optional[Union[_typing.KspOption, List[_typing.KspOption]]]) – A list of dicts corresponding to command line options for PETSc, used to compute the (shape) gradient. If this is None, either a direct or an iterative method is used (depending on the configuration, section OptimizationRoutine, key gradient_method).

  • desired_weights (Optional[List[float]]) – The desired weights for the cost functional.

  • control_bcs_list (Optional[Union[List[List[fenics.DirichletBC]], List[fenics.DirichletBC], fenics.DirichletBC]]) – A list of boundary conditions for the control variables. This is passed analogously to bcs_list. Default is None.

  • preconditioner_forms (Optional[List[ufl.Form]]) – The list of forms for the preconditioner. The default is None, so that the preconditioner matrix is the same as the system matrix.

  • pre_callback (Optional[Callable]) – A function (without arguments) that will be called before each solve of the state system

  • post_callback (Optional[Callable]) – A function (without arguments) that will be called after the computation of the gradient.

  • linear_solver (Optional[_utils.linalg.LinearSolver]) – The linear solver (KSP) which is used to solve the linear systems arising from the discretized PDE.

  • adjoint_linear_solver (Optional[_utils.linalg.LinearSolver]) – The linear solver (KSP) which is used to solve the (linear) adjoint system.

  • newton_linearizations (Optional[Union[ufl.Form, List[ufl.Form]]]) – A (list of) UFL forms describing which (alternative) linearizations should be used for the (nonlinear) state equations when solving them (with Newton’s method). The default is None, so that the Jacobian of the supplied state forms is used.

optimize()[source]#

Solves the coarse model optimization problem.

Return type:

None

class cashocs.space_mapping.optimal_control.FineModel[source]#

Bases: ABC

Base class for the fine model in space mapping.

Variables:

  • controls (List[fenics.Function]) – The control variables of the fine model.

  • cost_functional_value (float) – The current cost functional value of the fine model.

Initializes self.

abstract solve_and_evaluate()[source]#

Solves and evaluates the fine model.

This needs to be overwritten with a custom implementation.

Return type:

None

controls: List[fenics.Function]#
cost_functional_value: float#
class cashocs.space_mapping.optimal_control.ParameterExtraction(coarse_model, cost_functional_form, states, controls, config=None, desired_weights=None, mode='initial')[source]#

Bases: object

Parameter extraction for optimal control problems.

Initializes self.

Parameters:

  • coarse_model (CoarseModel) – The coarse model optimization problem

  • cost_functional_form (Union[List[_typing.CostFunctional], _typing.CostFunctional]) – The cost functional for the parameter extraction

  • states (Union[List[fenics.Function], fenics.Function]) – The state variables for the parameter extraction

  • controls (Union[List[fenics.Function], fenics.Function]) – The control variables for the parameter extraction

  • config (Optional[io.Config]) – config: The config file for the problem, generated via cashocs.load_config(). Alternatively, this can also be None, in which case the default configurations are used, except for the optimization algorithm. This has then to be specified in the solve method. The default is None.

  • desired_weights (Optional[List[float]]) – The list of desired weights for the parameter extraction

  • mode (str) – The mode used for the initial guess of the parameter extraction. If this is coarse_optimum, the default, then the coarse model optimum is used as initial guess, if this is initial, then the initial guess for the optimization is used.

class cashocs.space_mapping.optimal_control.SpaceMappingProblem(fine_model, coarse_model, parameter_extraction, method='broyden', max_iter=25, tol=0.01, use_backtracking_line_search=False, broyden_type='good', cg_type='FR', memory_size=10, scaling_factor=1.0, verbose=True, save_history=False)[source]#

Bases: object

Space mapping method for optimal control problems.

Initializes self.

Parameters:

  • fine_model (FineModel) – The fine model optimization problem

  • coarse_model (CoarseModel) – The coarse model optimization problem

  • parameter_extraction (ParameterExtraction) – The parameter extraction problem

  • method (Literal['broyden', 'bfgs', 'lbfgs', 'sd', 'steepest_descent', 'ncg']) – A string, which indicates which method is used to solve the space mapping. Can be one of “broyden”, “bfgs”, “lbfgs”, “sd”, “steepest descent”, or “ncg”. Default is “broyden”.

  • max_iter (int) – Maximum number of space mapping iterations

  • tol (float) – The tolerance used for solving the space mapping iteration

  • use_backtracking_line_search (bool) – A boolean flag, which indicates whether a backtracking line search should be used for the space mapping.

  • broyden_type (Literal['good', 'bad']) – A string, either “good” or “bad”, determining the type of Broyden’s method used. Default is “good”

  • cg_type (Literal['FR', 'PR', 'HS', 'DY', 'HZ']) – A string, either “FR”, “PR”, “HS”, “DY”, “HZ”, which indicates which NCG variant is used for solving the space mapping. Default is “FR”

  • memory_size (int) – The size of the memory for Broyden’s method and the BFGS method

  • scaling_factor (float) – A factor, which can be used to appropriately scale the control variables between fine and coarse model.

  • verbose (bool) – A boolean flag which indicates, whether the output of the space mapping method should be verbose. Default is True.

  • save_history (bool) – A boolean flag which indicates, whether the history of the space mapping method should be saved to a .json file. Default is False.

inject_post_callback(function)[source]#

Changes the a-posteriori callback of the OptimizationProblem.

Parameters:

function (Callable | None) – A custom function without arguments, which will be called after the computation of the gradient(s)

Return type:

None

inject_pre_callback(function)[source]#

Changes the a-priori callback of the OptimizationProblem.

Parameters:

function (Callable | None) – A custom function without arguments, which will be called before each solve of the state system

Return type:

None

inject_pre_post_callback(pre_function, post_function)[source]#

Changes the a-priori (pre) and a-posteriori (post) callbacks of the problem.

Parameters:

  • pre_function (Callable | None) – A function without arguments, which is to be called before each solve of the state system

  • post_function (Callable | None) – A function without arguments, which is to be called after each computation of the (shape) gradient

Return type:

None

output()[source]#

Uses the output manager to save / show the current results.

Return type:

None

solve()[source]#

Solves the space mapping problem.

Return type:

None

test_for_nonconvergence()[source]#

Tests, whether maximum number of iterations are exceeded.

Return type:

None