pymor.reductors.data_driven

Module Contents

class pymor.reductors.data_driven.DataDrivenPODReductor(training_parameters, training_snapshots, regressor=None, T=None, time_vectorized=False, output_functional=None, input_scaler=None, output_scaler=None, product=None, pod_params=None)

Bases: DataDrivenReductor

Reductor building a reduced basis and relying on a machine learning surrogate.

In addition to the DataDrivenReductor, this reductor uses snapshot data in order to construct a reduced basis via POD and projects the snapshots onto the reduced basis to generate data for the machine learning training. The approach is described in [HU18]. See DataDrivenReductor for more details.

Parameters:

• training_parameters – Parameter values to use for training of the regressor.

• training_snapshots – VectorArray to use for the training of the regressor. Contains the solutions or outputs associated to the parameters in training_parameters. In the case of a time-dependent problem, the snapshots are assumed to be equidistant in time.

• regressor – See DataDrivenReductor.

• T – See DataDrivenReductor.

• time_vectorized – See DataDrivenReductor.

• output_functional – Operator mapping a given solution to the model output. In many applications, this will be a Functional, i.e. an Operator mapping to scalars. This is not required, however. The output functional will be projected automatically onto the reduced space.

• input_scaler – See DataDrivenReductor.

• output_scaler – See DataDrivenReductor.

• product – Inner product Operators defined on the discrete space the problem is posed on. Used for reduced basis computation via POD and or orthogonal projection onto the reduced basis.

• pod_params – Dict of additional parameters for the POD-method.

Methods

extend_training_data	Add sequences of parameters and corresponding snapshots to the training data.
reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce	Reduce by training a machine learning surrogate.

extend_training_data(parameters, snapshots)

Add sequences of parameters and corresponding snapshots to the training data.

reconstruct(u)

Reconstruct high-dimensional vector from reduced vector u.

reduce(**kwargs)

Reduce by training a machine learning surrogate.

Parameters:

kwargs – Additional arguments that will be passed to the fit method of the regressor.

Returns:

The data-driven reduced model.

class pymor.reductors.data_driven.DataDrivenReductor(training_parameters, training_snapshots, regressor=None, target_quantity='solution', T=None, time_vectorized=False, output_functional=None, input_scaler=None, output_scaler=None)

Bases: pymor.core.base.BasicObject

Reductor relying on a machine learning surrogate.

The reductor works for stationary as well as for instationary problems and returns a suitable model for the respective case.

Depending on the argument target_quantity, this reductor either approximates the solution or the output as a parametric quantity by training a machine learning surrogate.

In case of an approximation of the solution, the reductor trains a machine learning regressor that approximates the mapping from parameter space to a NumPy array. Typically, the array contains coefficients of the solution with respect to a reduced basis.

For target_quantity='output', the machine learning regressor directly approximates the output depending on the parameter. The outputs for the training parameters are either computed using the full-order model or can be provided as the training_snapshots argument.

Parameters:

• training_parameters – Parameter values to use for training of the regressor.

• training_snapshots – Iterable containing the training snapshots of the regressor. Contains the solutions (reduced coefficients w.r.t. the reduced basis or outputs) associated to the parameters in training_parameters. In the case of a time-dependent problem, the snapshots are assumed to be equidistant in time.

• regressor – Regressor with fit and predict methods similar to scikit-learn regressors that is trained in the reduce-method. If None (which is also the default), a VKOGARegressor is used.

• target_quantity – Either 'solution' or 'output', determines which quantity to learn.

• T – In the instationary case, determines the final time until which to solve.

• time_vectorized – In the instationary case, determines whether to predict the whole time trajectory at once (time-vectorized version; output of the regressor is typically very high-dimensional in this case) or if the result for a single point in time is approximated (time serves as an additional input to the regressor).

• output_functional – Operator mapping a given solution to the model output. In many applications, this will be a Functional, i.e. an Operator mapping to scalars. This is not required, however.

• input_scaler – If not None, a scaler object with fit, transform and inverse_transform methods similar to the scikit-learn interface can be used to scale the parameters before passing them to the regressor.

• output_scaler – If not None, a scaler object with fit, transform and inverse_transform methods similar to the scikit-learn interface can be used to scale the outputs (reduced coeffcients or output quantities) before passing them to the regressor.

Methods

extend_training_data	Add sequences of parameters and corresponding snapshots to the training data.
reduce	Reduce by training a machine learning surrogate.

extend_training_data(parameters, snapshots)

Add sequences of parameters and corresponding snapshots to the training data.

reduce(**kwargs)

Reduce by training a machine learning surrogate.

Parameters:

kwargs – Additional arguments that will be passed to the fit method of the regressor.

Returns:

The data-driven reduced model.