pymor.models.interface

Module Contents

class pymor.models.interface.Model(dim_input=0, products=None, error_estimator=None, visualizer=None, name=None)

Bases: pymor.core.cache.CacheableObject, pymor.parameters.base.ParametricObject

Interface for model objects.

A model object defines a discrete problem via its class and the Operators it contains. Furthermore, models can be solved for given parameter values resulting in a solution VectorArray.

solution_space

VectorSpace of the solution VectorArrays returned by solve.

dim_output

Dimension of the model output returned by output. 0 if the model has no output.

linear

True if the model describes a linear problem.

products

Dict of inner product operators associated with the model.

order

Dimension of the solution_space.

Methods

compute	Compute the solution of the model and associated quantities.
estimate_error	Estimate the error for the computed internal state.
estimate_output_error	Estimate the error for the computed output.
output	Return the model output for given parameter values mu.
output_d_mu	Compute the gradient w.r.t. the parameter of the output functional.
solve	Solve the discrete problem for the parameter values mu.
solve_d_mu	Solve for the partial derivative of the solution w.r.t. a parameter index
visualize	Visualize a VectorArray U of the model's solution_space.

compute(solution=False, output=False, solution_d_mu=False, output_d_mu=False, solution_error_estimate=False, output_error_estimate=False, output_d_mu_return_array=False, output_error_estimate_return_vector=False, *, mu=None, input=None, **kwargs)

Compute the solution of the model and associated quantities.

This method computes the output of the model, its internal state, and various associated quantities for given parameter values mu.

Note

The default implementation defers the actual computations to the methods _compute_solution, _compute_output, _compute_solution_error_estimate and _compute_output_error_estimate. The call to _compute_solution is cached. In addition, Model implementors may implement _compute to simultaneously compute multiple values in an optimized way. The corresponding _compute_XXX methods will not be called for values already returned by _compute.

Parameters

solution

If True, return the model’s internal state.

output

If True, return the model output.

solution_d_mu

If not False, either True to return the derivative of the model’s internal state w.r.t. all parameter components or a tuple (parameter, index) to return the derivative of a single parameter component.

output_d_mu

If True, return the gradient of the model output w.r.t. the Parameter.

solution_error_estimate

If True, return an error estimate for the computed internal state.

output_error_estimate

If True, return an error estimate for the computed output.

output_d_mu_return_array

If True, return the output gradient as a NumPy array. Otherwise, return a dict of gradients for each Parameter.

output_error_estimate_return_vector

If True, return the output estimate as a NumPy array, where each component corresponds to the respective component of the output_functional. Otherwise, return the Euclidean norm of all components.

mu

Parameter values for which to compute the values.

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

kwargs

Further keyword arguments to select further quantities that should be returned or to customize how the values are computed.

Returns

A dict with the computed values.

estimate_error(mu=None, input=None, **kwargs)

Estimate the error for the computed internal state.

For given parameter values mu this method returns an error estimate for the computed internal model state as returned by solve. It is a convenience wrapper around compute.

The model error could be the error w.r.t. the analytical solution of the given problem or the model reduction error w.r.t. a corresponding high-dimensional Model.

Parameters

mu

Parameter values for which to estimate the error.

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

kwargs

Additional keyword arguments passed to compute that might affect how the error estimate (or the solution) is computed.

Returns

The estimated error.

estimate_output_error(mu=None, input=None, return_vector=False, **kwargs)

Estimate the error for the computed output.

For given parameter values mu this method returns an error estimate for the computed model output as returned by output. It is a convenience wrapper around compute.

The output error could be the error w.r.t. the analytical solution of the given problem or the model reduction error w.r.t. a corresponding high-dimensional Model.

Parameters

mu

Parameter values for which to estimate the error.

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

return_vector

If True, return the output estimate as a NumPy array, where each component corresponds to the respective component of the output_functional. Otherwise, return the Euclidean norm of all components.

kwargs

Additional keyword arguments passed to compute that might affect how the error estimate (or the output) is computed.

Returns

The estimated error.

output(mu=None, input=None, return_error_estimate=False, return_error_estimate_vector=False, **kwargs)

Return the model output for given parameter values mu.

This method is a convenience wrapper around compute.

Parameters

mu

Parameter values for which to compute the output.

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

return_error_estimate

If True, also return an error estimate for the computed output.

return_error_estimate_vector

If True, return the output estimate as a NumPy array, where each component corresponds to the respective component of the output_functional. Otherwise, return the Euclidean norm of all components.

kwargs

Additional keyword arguments passed to compute that might affect how the solution is computed.

Returns

The computed model output as a 2D NumPy array. The dimension of axis 1 is : attr:dim_output. (For stationary problems, axis 0 has dimension 1. For time-dependent problems, the dimension of axis 0 depends on the number of time steps.) When return_error_estimate is True, the estimate is returned as second value.

output_d_mu(mu=None, input=None, return_array=False, **kwargs)

Compute the gradient w.r.t. the parameter of the output functional.

Parameters

mu

Parameter value for which to compute the gradient

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

return_array

if True, return the output gradient as a NumPy array. Otherwise, return a dict of gradients for each Parameter.

Returns

The gradient as a NumPy array or a dict of NumPy arrays.

solve(mu=None, input=None, return_error_estimate=False, **kwargs)

Solve the discrete problem for the parameter values mu.

This method returns a VectorArray with a internal state representation of the model’s solution for given parameter values. It is a convenience wrapper around compute.

The result may be cached in case caching has been activated for the given model.

Parameters

mu

Parameter values for which to solve.

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

return_error_estimate

If True, also return an error estimate for the computed solution.

kwargs

Additional keyword arguments passed to compute that might affect how the solution is computed.

Returns

The solution VectorArray. When return_error_estimate is True, the estimate is returned as second value.

solve_d_mu(parameter, index, mu=None, input=None, **kwargs)

Solve for the partial derivative of the solution w.r.t. a parameter index

Parameters

parameter

parameter for which to compute the sensitivity

index

parameter index for which to compute the sensitivity

mu

Parameter value for which to solve

input

The model input. Either a NumPy array of shape (self.dim_input,), a Function with dim_domain == 1 and shape_range == (self.dim_input,) mapping time to input, or a str expression with t as variable that can be used to instantiate an ExpressionFunction of this type. Can be None if self.dim_input == 0.

Returns

The sensitivity of the solution as a VectorArray.

visualize(U, **kwargs)

Visualize a VectorArray U of the model’s solution_space.

Parameters

U

The VectorArray from solution_space that shall be visualized.

kwargs

Additional keyword arguments to customize the visualization. See the docstring of self.visualizer.visualize.