MDA algorithms¶

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Note

All the features of the wrapped libraries may not be exposed through GEMSEO.

MDAChain¶

Module: gemseo.mda.mda_chain

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

chain_linearize : bool, optional

Whether to linearize the chain of execution. Otherwise, linearize the overall MDA with base class method. This last option is preferred to minimize computations in adjoint mode, while in direct mode, linearizing the chain may be cheaper.

By default it is set to False.
coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
initialize_defaults : bool, optional

Whether to create a MDOInitializationChain to compute the eventually missing default_inputs at the first execution.

By default it is set to False.
inner_mda_name : str, optional

The class name of the inner-MDA.

By default it is set to MDAJacobi.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
log_convergence : bool, optional

Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 20.
mdachain_parallel_options : Mapping[str, int | bool] | None, optional

The options of the MDOParallelChain instances, if any.

By default it is set to None.
mdachain_parallelize_tasks : bool, optional

Whether to parallelize the parallel tasks, if any.

By default it is set to False.
n_processes : int, optional

The maximum simultaneous number of threads if use_threading is set to True, otherwise processes, used to parallelize the execution.

By default it is set to 2.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
sub_coupling_structures : Iterable[MDOCouplingStructure | None] | None, optional

The coupling structures to be used by the inner-MDAs. If None, they are created from the sub-disciplines.

By default it is set to None.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
**inner_mda_options : float | int | bool | str | None

The options of the inner-MDAs.

MDAGSNewton¶

Module: gemseo.mda.sequential_mda

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
log_convergence : bool, optional

Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
max_mda_iter_gs : int, optional

The maximum number of iterations of the Gauss-Seidel MDA.

By default it is set to 3.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
relax_factor : float, optional

The relaxation factor.

By default it is set to 0.99.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.
**newton_mda_options : float | str | None

The options for the Newton MDA.

MDAGaussSeidel¶

Module: gemseo.mda.gauss_seidel

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

acceleration_method : AccelerationMethod, optional

The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to NoTransformation.
coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
log_convergence : bool, optional

Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
over_relax_factor : float | None, optional

Deprecated, please consider using MDA.over_relaxation_factor instead. The relaxation coefficient, used to make the method more robust, if 0<over_relax_factor<1 or faster if 1<over_relax_factor<=2. If over_relax_factor =1., it is deactivated.

By default it is set to None.
over_relaxation_factor : float, optional

The over-relaxation factor.

By default it is set to 1.0.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

MDAJacobi¶

Module: gemseo.mda.jacobi

Required parameters

acceleration : str

Deprecated, please consider using the MDA.acceleration_method instead. The type of acceleration to be used to extrapolate the residuals and save CPU time by reusing the information from the last iterations, either None, "m2d", or "secant", "m2d" is faster but uses the 2 last iterations.
disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

acceleration_method : AccelerationMethod, optional

The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to Alternate2Delta.
coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
log_convergence : bool, optional

Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
n_processes : int, optional

The maximum simultaneous number of threads if use_threading is set to True, otherwise processes, used to parallelize the execution.

By default it is set to 2.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
over_relaxation_factor : float, optional

The over-relaxation factor.

By default it is set to 1.0.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
use_threading : bool, optional

Whether to use threads instead of processes to parallelize the execution. Processes will copy (serialize) all the disciplines, while threads will share all the memory. If one wants to execute the same discipline multiple times then multiprocessing should be prefered.

By default it is set to True.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

MDANewtonRaphson¶

Module: gemseo.mda.newton_raphson

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

acceleration_method : AccelerationMethod, optional

The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to NoTransformation.
coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
log_convergence : bool, optional

Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
n_processes : int, optional

The maximum simultaneous number of threads if use_threading is set to True, otherwise processes, used to parallelize the execution.

By default it is set to 2.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
newton_linear_solver_name : str, optional

The name of the linear solver for the Newton method.

By default it is set to DEFAULT.
newton_linear_solver_options : Mapping[str, Any] | None, optional

The options for the Newton linear solver.

By default it is set to None.
over_relaxation_factor : float, optional

The over-relaxation factor.

By default it is set to 0.99.
parallel : bool, optional

Whether to execute and linearize the disciplines in parallel.

By default it is set to False.
relax_factor : float | None, optional

The relaxation factor.

By default it is set to None.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
use_threading : bool, optional

Whether to use threads instead of processes to parallelize the execution. Processes will copy (serialize) all the disciplines, while threads will share all the memory. If one wants to execute the same discipline multiple times then multiprocessing should be preferred.

By default it is set to True.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

MDAQuasiNewton¶

Module: gemseo.mda.quasi_newton

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

Optional parameters

coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
method : str, optional

The name of the method in scipy root finding, among QUASI_NEWTON_METHODS.

By default it is set to hybr.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_gradient : bool, optional

Whether to use the analytic gradient of the discipline.

By default it is set to False.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

MDASequential¶

Module: gemseo.mda.sequential_mda

Required parameters

disciplines : Sequence[MDODiscipline]

The disciplines from which to compute the MDA.
mda_sequence : Sequence[MDA]

The sequence of MDAs.

Optional parameters

coupling_structure : MDOCouplingStructure | None, optional

The coupling structure to be used by the MDA. If None, it is created from disciplines.

By default it is set to None.
grammar_type : MDODiscipline.GrammarType, optional

The type of the input and output grammars.

By default it is set to JSONGrammar.
linear_solver : str, optional

The name of the linear solver.

By default it is set to DEFAULT.
linear_solver_options : Mapping[str, Any] | None, optional

The options passed to the linear solver factory.

By default it is set to None.
linear_solver_tolerance : float, optional

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.
max_mda_iter : int, optional

The maximum iterations number for the MDA algorithm.

By default it is set to 10.
name : str | None, optional

The name to be given to the MDA. If None, use the name of the class.

By default it is set to None.
tolerance : float, optional

The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

By default it is set to 1e-06.
use_lu_fact : bool, optional

Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

By default it is set to False.
warm_start : bool, optional

Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.