gemseo / mda

# quasi_newton module¶

A set of quasi Newton algorithm variants for solving MDAs.

quasi-Newton methods

class gemseo.mda.quasi_newton.MDAQuasiNewton(disciplines, max_mda_iter=10, name='', grammar_type=GrammarType.JSON, method=QuasiNewtonMethod.HYBRID, use_gradient=False, tolerance=1e-06, linear_solver_tolerance=1e-12, warm_start=False, use_lu_fact=False, coupling_structure=None, linear_solver='DEFAULT', linear_solver_options=None)[source]

Bases: BaseMDARoot

Quasi-Newton solver for MDA.

Quasi-Newton methods include numerous variants ( Broyden, Levenberg-Marquardt <https://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm> __, …).

The name of the variant should be provided via the method parameter of the class.

The new iterate is given by:

$\begin{split}x_{k+1} = x_k - \\rho_k B_k f(x_k)\end{split}$

where $$\\rho_k$$ is a coefficient chosen in order to minimize the convergence and $$B_k$$ is an approximation of $$Df(x_k)^{-1}$$, the inverse of the Jacobian of $$f$$ at $$x_k$$.

Initialize self. See help(type(self)) for accurate signature.

Parameters:
• disciplines (Sequence[MDODiscipline]) – The disciplines from which to compute the MDA.

• max_mda_iter (int) –

The maximum iterations number for the MDA algorithm.

By default it is set to 10.

• name (str) –

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

By default it is set to “”.

• grammar_type (MDODiscipline.GrammarType) –

The type of the input and output grammars.

By default it is set to “JSONGrammar”.

• method (QuasiNewtonMethod) –

The name of the method in scipy root finding.

By default it is set to “hybr”.

Whether to use the analytic gradient of the discipline.

By default it is set to False.

• tolerance (float) –

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.

• linear_solver_tolerance (float) –

The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

• warm_start (bool) –

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

By default it is set to False.

• use_lu_fact (bool) –

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.

• coupling_structure (MDOCouplingStructure | None) – The coupling structure to be used by the MDA. If None, it is created from disciplines.

• linear_solver (str) –

The name of the linear solver.

By default it is set to “DEFAULT”.

• linear_solver_options (StrKeyMapping | None) – The options passed to the linear solver factory.

Raises:

ValueError – If the method is not a valid quasi-Newton method.

class QuasiNewtonMethod(value)[source]

Bases: StrEnum

A quasi-Newton method.

ANDERSON = 'anderson'
BROYDEN1 = 'broyden1'
BROYDEN2 = 'broyden2'
DF_SANE = 'df-sane'
DIAG_BROYDEN = 'diagbroyden'
EXCITING_MIXING = 'excitingmixing'
HYBRID = 'hybr'
KRYLOV = 'krylov'
LEVENBERG_MARQUARDT = 'lm'
LINEAR_MIXING = 'linearmixing'
all_couplings: list[str]

The names of all the coupling variables.

assembly: JacobianAssembly
cache: BaseCache | None

The cache containing one or several executions of the discipline according to the cache policy.

coupling_structure: MDOCouplingStructure

The coupling structure to be used by the MDA.

data_processor: DataProcessor

A tool to pre- and post-process discipline data.

exec_for_lin: bool

Whether the last execution was due to a linearization.

input_grammar: BaseGrammar

The input grammar.

jac: MutableMapping[str, MutableMapping[str, ndarray | csr_array | JacobianOperator]]

The Jacobians of the outputs wrt inputs.

The structure is {output: {input: matrix}}.

lin_cache_tol_fact: float

The tolerance factor to cache the Jacobian.

linear_solver: str

The name of the linear solver.

linear_solver_options: StrKeyMapping

The options of the linear solver.

linear_solver_tolerance: float

The tolerance of the linear solver in the adjoint equation.

matrix_type: JacobianAssembly.JacobianType

The type of the matrix.

n_processes: int

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

name: str

The name of the discipline.

norm0: float | None

The reference residual, if any.

normed_residual: float

The normed residual.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

reset_history_each_run: bool

Whether to reset the history of MDA residuals before each run.

residual_history: list[float]

The history of the MDA residuals.

residual_variables: dict[str, str]

The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.

run_solves_residuals: bool

Whether the run method shall solve the residuals.

scaling: ResidualScaling

The scaling method applied to MDA residuals for convergence monitoring.

strong_couplings: list[str]

The names of the strong coupling variables.

tolerance: float

The tolerance of the iterative direct coupling solver.

use_lu_fact: bool

Whether to store a LU factorization of the matrix.