pymor.models.interface
¶
Module Contents¶
- class pymor.models.interface.Model(dim_input=0, products=None, error_estimator=None, visualizer=None, name=None)[source]¶
Bases:
pymor.core.cache.CacheableObject
,pymor.parameters.base.ParametricObject
Interface for model objects.
A model object defines a discrete problem via its
class
and theOperators
it contains. Furthermore, models can besolved
for givenparameter values
resulting in a solutionVectorArray
.- solution_space[source]¶
VectorSpace
of the solutionVectorArrays
returned bysolve
.
Methods
Compute the solution of the model and associated quantities.
Estimate the error for the computed internal state.
Estimate the error for the computed output.
Return the model output for given
parameter values
mu
.Compute the gradient w.r.t. the parameter of the output functional.
Solve the discrete problem for the
parameter values
mu
.Solve for the partial derivative of the solution w.r.t. a parameter index
Visualize a
VectorArray
U of the model'ssolution_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)[source]¶
Compute the solution of the model and associated quantities.
This methods computes the output of the model it’s 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
iscached
. 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
, eitherTrue
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. theParameter
.- 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 aNumPy array
. Otherwise, return a dict of gradients for eachParameter
.- output_error_estimate_return_vector
If
True
, return the output estimate as aNumPy array
, where each component corresponds to the respective component of theoutput_functional
. Otherwise, return the euclidian 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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.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)[source]¶
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 bysolve
. It is a convenience wrapper aroundcompute
.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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.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)[source]¶
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 byoutput
. It is a convenience wrapper aroundcompute
.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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.- return_vector
If
True
, return the output estimate as aNumPy array
, where each component corresponds to the respective component of theoutput_functional
. Otherwise, return the euclidian 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)[source]¶
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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.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 aNumPy array
, where each component corresponds to the respective component of theoutput_functional
. Otherwise, return the euclidian 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.) Whenreturn_error_estimate
isTrue
, the estimate is returned as second value.
- output_d_mu(mu=None, input=None, return_array=False, **kwargs)[source]¶
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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.- return_array
if
True
, return the output gradient as aNumPy array
. Otherwise, return a dict of gradients for eachParameter
.
Returns
The gradient as a
NumPy array
or a dict ofNumPy arrays
.
- solve(mu=None, input=None, return_error_estimate=False, **kwargs)[source]¶
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 givenparameter values
. It is a convenience wrapper aroundcompute
.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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.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
. Whenreturn_error_estimate
isTrue
, the estimate is returned as second value.
- solve_d_mu(parameter, index, mu=None, input=None, **kwargs)[source]¶
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,)
, aFunction
withdim_domain == 1
andshape_range == (self.dim_input,)
mapping time to input, or astr
expression whitht
as variable that can be used to instatiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.
Returns
The sensitivity of the solution as a
VectorArray
.
- visualize(U, **kwargs)[source]¶
Visualize a
VectorArray
U of the model’ssolution_space
.Parameters
- U
The
VectorArray
fromsolution_space
that shall be visualized.- kwargs
Additional keyword arguments to customize the visualization. See the docstring of
self.visualizer.visualize
.