DiscreteModel

class DiscreteModel(operators)

Nonparametric discrete dynamical system model \(\qhat_{j+1} = \fhat(\qhat_{j}, \u_{j})\).

Here,

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

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

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

Parameters

operatorslist of opinf.operators objects

Operators comprising the terms of the model.

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).
data_matrix_	\(k \times d(r, m)\) data matrix, e.g., \(\D = [~ \mathbf{1}~~ \widehat{\Q}\trp~~ (\widehat{\Q}\odot\widehat{\Q})\trp~~ \U\trp~]\).
input_dimension	Dimension \(m\) of the input (zero if there are no inputs).
operator_matrix_	\(r \times d(r, m)\) operator matrix, e.g., \(\Ohat = [~\chat~~\Ahat~~\Hhat~~\Bhat~]\).
operator_matrix_dimension	Number of columns \(d(r, m)\) of the operator matrix \(\Ohat\) and the data matrix \(\D\), i.e., the number of unknowns in the Operator Inference regression problem for each system mode.
operators	Operators comprising the terms of the model.
state_dimension	Dimension \(r\) of the state.

Methods

copy	Make a copy of the model.
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.
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.
stack_trajectories	Translate a collection of state trajectories and (optionally) inputs to arrays that are appropriate arguments for fit().