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
Set of quantities that can be compute via
compute
.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 output sensitivities w.r.t. the model's parameters.
Solve the discrete problem for the
parameter values
mu
.Compute the solution sensitivity w.r.t. a single parameter.
Visualize a
VectorArray
U of the model'ssolution_space
.- compute(data=None, *, solution=False, output=False, solution_d_mu=False, output_d_mu=False, solution_error_estimate=False, output_error_estimate=False, mu=None, input=None, **kwargs)[source]¶
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
.Parameters
- data
If not
None
, a dict of already computed quantities for the givenmu
andinput
. If used, newly computed quantities are added to the given dict and the same dict is returned. Providing adata
dict can be helpful when some quantities (e.g.,output
) depend on already known quantities (e.g,solution
) and caching has not been activated.- 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 sensitivities of the model’s solution w.r.t. all parameters, or a sequence of tuples(parameter, index)
to compute the solution sensitivities for selected parameters.- output_d_mu
If
True
, return the output sensitivities w.r.t. the model’s parameters.- 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.- 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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.- kwargs
Additional keyword arguments to select further quantities that should be computed.
Returns
A dict with the computed values.
- estimate_error(mu=None, input=None)[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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.
Returns
The estimated : attr:
solution_space
error as a 1DNumPy array
. For stationary problems, the returned array has length 1. For time-dependent problems, the length depends on the number of time steps. The norm w.r.t. which the error is estimated depends on the given problem.
- estimate_output_error(mu=None, input=None)[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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.
Returns
The estimated 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. The spatial/temporal norms w.r.t. which the error is estimated depend on the given problem.
- output(mu=None, input=None, return_error_estimate=False)[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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.- return_error_estimate
If
True
, also return an error estimate for the computed output.
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)[source]¶
Compute the output sensitivities w.r.t. the model’s parameters.
Parameters
- mu
Parameter value
at which to compute the output sensitivities.- 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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.
Returns
The output sensitivities as a dict
{(parameter, index) : sensitivity}
wheresensitivity
is a 2DNumPy arrays
with axis 0 corresponding to time and axis 1 corresponding to the output component. The returned : class:OutputDMuResult
object has ameth
:~OutputDMuResult.to_numpy` method to convert it into a single NumPy array, e.g., for use in optimization libraries.
- solve(mu=None, input=None, return_error_estimate=False)[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 witht
as variable that can be used to instantiate anExpressionFunction
of this type. Can beNone
ifself.dim_input == 0
.- return_error_estimate
If
True
, also return an error estimate for the computed solution.
Returns
The solution
VectorArray
. Whenreturn_error_estimate
isTrue
, the estimate is returned as second value.
- solve_d_mu(parameter, index, mu=None, input=None)[source]¶
Compute the solution sensitivity w.r.t. a single parameter.
Parameters
- parameter
Parameter for which to compute the sensitivity.
- index
Parameter index for which to compute the sensitivity.
- mu
Parameter value
at which to compute the sensitivity.- 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 witht
as variable that can be used to instantiate 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
.
- class pymor.models.interface.OutputDMuResult(*args, **kwargs)[source]¶
Bases:
pymor.tools.frozendict.FrozenDict
Immutable dict of gradients returned by
output_d_mu
.Methods
Return gradients as a single 3D NumPy array.