pymor.algorithms.tr

Module Contents

class pymor.algorithms.tr.BasicTRSurrogate(reductor, initial_guess, name=None)

Bases: TRSurrogate

Surrogate for trust_region only enriching with the primal solution.

Parameters:

• reductor – The reductor used to generate the reduced order models and estimate the output error.

• initial_guess – The parameter values containing an initial guess for the optimal parameter value.

Methods

extend

Extend the current ROM for new parameter values.

extend(mu)

Extend the current ROM for new parameter values.

Parameters:

mu – The Mu instance for which an extension is computed.

class pymor.algorithms.tr.PrimalDualTRSurrogate(reductor, initial_guess, name=None)

Bases: TRSurrogate

Surrogate for trust_region enriching with both the primal and dual solutions.

Parameters:

• reductor – The reductor used to generate the reduced order models and estimate the output error.

• initial_guess – The parameter values containing an initial guess for the optimal parameter value.

Methods

extend

Extend the current ROM for new parameter values with primal and dual solutions.

extend(mu)

Extend the current ROM for new parameter values with primal and dual solutions.

Parameters:

mu – The Mu instance for which an extension is computed.

class pymor.algorithms.tr.QuadraticOutputTRSurrogate(reductor, initial_guess, continuity_estimator_output, product_name=None)

Bases: BasicTRSurrogate

Surrogate for trust_region with only the primal enrichment naive output estimate.

Note

This specialized TRSurrogate should soon be made obsolete when the quadratic output estimation is included into a reductor.

Parameters:

• reductor – The reductor used to generate the reduced order models and estimate the output error.

• initial_guess – The parameter values containing an initial guess for the optimal parameter value.

• continuity_estimator_output – Estimation for the continuity constant of the quadratic output functional.

• product_name – Name of the inner-product Operator of the ROM w.r.t. which the continuity constant for the output is estimated.

Methods

estimate_output_error

estimate_output_error(mu)

class pymor.algorithms.tr.TRSurrogate(reductor, initial_guess, name=None)

Bases: pymor.core.base.BasicObject

Base class for trust_region surrogates.

Not to be used directly.

Methods

accept	Accept the new ROM.
estimate_output_error
extend
new_output
output
output_d_mu
rb_size
reject	Reject the new ROM.

accept()

Accept the new ROM.

This function is intended to be called after extend was called.

estimate_output_error(mu)

abstract extend(mu)

new_output(mu)

output(mu)

output_d_mu(mu)

rb_size()

reject()

Reject the new ROM.

This function is intended to be called after extend was called.

pymor.algorithms.tr.coercive_rb_trust_region(reductor, primal_dual=False, parameter_space=None, initial_guess=None, beta=0.95, radius=0.1, shrink_factor=0.5, miniter=0, maxiter=30, miniter_subproblem=0, maxiter_subproblem=400, tol_criticality=1e-06, radius_tol=0.75, rtol_output=1e-16, rtol_mu=1e-16, tol_sub=1e-08, armijo_alpha=0.0001, line_search_params=None, stagnation_window=3, stagnation_threshold=np.inf, quadratic_output=False, quadratic_output_continuity_estimator=None, quadratic_output_product_name=None)

Error aware trust-region method for a coercive RB model as surrogate.

See trust_region.

Parameters:

• reductor – The reductor used to generate the reduced order models and estimate the output error.

• primal_dual – If False, only enrich with the primal solution. If True, additionally enrich with the dual solutions.

• quadratic_output – Set to True if output is given by a quadratic functional.

• quadratic_output_continuity_estimator – In case of a quadratic output functional, a ParameterFunctional giving an upper bound for the norm of the corresponding bilinear form.

• quadratic_output_product_name – In case of a quadratic output functional, the name of the inner-product Operator of the ROM w.r.t. which the continuity constant for the output is estimated.

pymor.algorithms.tr.trust_region(fom, surrogate, parameter_space=None, initial_guess=None, beta=0.95, radius=0.1, shrink_factor=0.5, miniter=0, maxiter=30, miniter_subproblem=0, maxiter_subproblem=400, tol_criticality=1e-06, radius_tol=0.75, rtol_output=1e-16, rtol_mu=1e-16, tol_sub=1e-08, armijo_alpha=0.0001, line_search_params=None, stagnation_window=3, stagnation_threshold=np.inf)

Error-aware trust region algorithm.

This method solves the optimization problem

min J(mu), mu in C

for a model with an output \(J\) depending on a box-constrained mu using an adaptive trust region method.

The main idea for the algorithm can be found in [YM13], and an application to box-constrained parameters with possible enlarging of the trust radius in [KMO+21].

This method contrasts itself from scipy.optimize.minimize in the computation of the trust region: scipy TR implementations use a metric distance, whereas this function uses an error estimator obtained from the surrogate. Additionally, the cheap model function surrogate here is only updated for each outer iteration, not entirely reconstructed.

Parameters:

• fom – The Model with output J used for the optimization.

• surrogate – The TRSurrogate used to generate the surrogate model and estimate the output error.

• parameter_space – If not None, the ParameterSpace for enforcing the box constraints on the parameter values mu. Otherwise a ParameterSpace with lower bound -1 and upper bound 1 is used.

• initial_guess – If not None, parameter values containing an initial guess for the solution mu. Otherwise, random parameter values from the parameter_space are chosen as the initial value.

• beta – The factor used to check if the current parameter values are close to the trust region boundary.

• radius – The radius of the initial trust region.

• shrink_factor – The factor by which the trust region is shrunk. If the trust region radius is increased, it is increased by 1. / shrink_factor.

• miniter – Minimum amount of iterations to perform.

• maxiter – Fail if the iteration count reaches this value without converging.

• miniter_subproblem – Minimum amount of iterations to perform in the BFGS subproblem.

• maxiter_subproblem – Fail the BFGS subproblem if the iteration count reaches this value without converging.

• tol_criticality – Finish when the current parameter values fulfill the approximate first order critical optimality condition with a value below this threshold.

• radius_tol – Threshold for increasing the trust region radius upon extending the reduced order model.

• rtol_output – See rtol_output of error_aware_bfgs.

• rtol_mu – See rtol_mu of error_aware_bfgs.

• tol_sub – See tol_sub of error_aware_bfgs.

• armijo_alpha – Threshold for the constrained Armijo condition. See constrained_armijo.

• line_search_params – Dictionary of additional parameters passed to the Armijo line search method.

• stagnation_window – Finish when the parameter update has not been enlarged by a factor of stagnation_threshold during the last stagnation_window iterations.

• stagnation_threshold – See stagnation_window.

Returns:

• mu – NumPy array containing the computed optimal parameter values.

• data – Dict containing additional information of the optimization call.

Raises:

TRError – Raised if the TR algorithm failed to converge.