InterpDiscreteModel

class InterpDiscreteModel(operators, solver=None, InterpolatorClass=None)

Parametric discrete dynamical system model \(\qhat(\bfmu)_{j+1} = \fhat(\qhat(\bfmu)_{j}, \u_{j}; \bfmu)\) where the parametric dependence is handled by elementwise interpolation.

Here,

• \(\qhat_j\in\RR^{r}\) is the \(j\)-th iteration of the model state,

• \(\u_j\in\RR^{m}\) is the (optional) corresponding input, and

• \(\bfmu\in\RR^{p}\in\RR^{p}\) is the parameter vector.

The structure of \(\fhat\) is specified through the operators attribute.

Parameters:

operatorslist of opinf.operators objects

Operators comprising the terms of the model. For this class, these must be interpolated parametric operators.

InterpolatorClasstype or None

Class for the elementwise interpolation. Must obey the syntax

>>> interpolator = InterpolatorClass(data_points, data_values)
>>> interpolator_evaluation = interpolator(new_data_point)

This can be, e.g., a class from scipy.interpolate. If None (default), use scipy.interpolate.CubicSpline for one-dimensional parameters and scipy.interpolate.LinearNDInterpolator otherwise.

Properties:

A_

opinf.operators.LinearOperator (or None).

B_

opinf.operators.InputOperator (or None).

G_

opinf.operators.CubicOperator (or None).

H_

opinf.operators.QuadraticOperator (or None).

N_

opinf.operators.StateInputOperator (or None).

c_

opinf.operators.ConstantOperator (or None).

input_dimension

Dimension \(m\) of the input (zero if there are no inputs).

operators

Operators comprising the terms of the model.

parameter_dimension

Dimension \(p\) of a parameter vector \(\bfmu\).

solver

Solver for the least-squares regression, see opinf.lstsq.

state_dimension

Dimension \(r\) of the state.

Methods:

copy	Make a copy of the model.
evaluate	Construct a nonparametric model by fixing the parameter value.
fit	Learn the model operators from data.
galerkin	Construct a reduced-order model by taking the (Petrov-)Galerkin projection of each model operator.
jacobian	Sum the state Jacobian of each model operator.
load	Load a serialized model from an HDF5 file, created previously from the save() method.
predict	Step forward the discrete dynamical system niters steps.
refit	Evaluate the least-squares solver and process the results.
rhs	Evaluate the right-hand side of the model by applying each operator and summing the results.
save	Serialize the model, saving it in HDF5 format.
set_interpolator	Set the interpolator for the operator entries.