DiscreteModel

class DiscreteModel(operators, solver=None)

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.

solveropinf.lstsq object or float > 0 or None

Solver for the least-squares regression. Defaults:

• None: opinf.lstsq.PlainSolver. SVD-based solve without regularization.

• float > 0: opinf.lstsq.L2Solver. SVD-based solve with scalar Tikhonov regularization.

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).

operator_matrix

\(r \times d(r, m)\) operator matrix, e.g., \(\Ohat = [~\chat~~\Ahat~~\Hhat~~\Bhat~]\).

This matrix does not includes the entries of any operators whose entries are known a priori.

operators

Operators comprising the terms of the model.

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.
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	Solve the Operator Inference regression using the data from the last fit() call, then extract the inferred operators.
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().