ParametricOperatorTemplate

class ParametricOperatorTemplate

Template for operators that depend on external parameters, \(\Ophat_{\ell}(\qhat,\u;\bfmu).\)

In this package, a parametric “operator” is a function \(\Ophat_{\ell}: \RR^r \times \RR^m \times \RR^p \to \RR^r\) that acts on a state vector \(\qhat\in\RR^r\), an (optional) input vector \(\u\in\RR^m\), and a parameter vector \(\bfmu\in\RR^p\).

Parametric models are defined as the sum of several operators, at least one of which is parametric. For example, a system of ODEs:

\[\ddt\qhat(t;\bfmu) = \sum_{\ell=1}^{n_\textrm{terms}}\Ophat_{\ell}(\qhat(t),\u(t);\bfmu).\]

Notes

This class can be used for custom nonparametric model terms that are not learnable with Operator Inference. For nonparametric model terms, see OperatorTemplate. For model terms that can be learned with Operator Inference, see OpInfOperator or ParametricOpInfOperator.

Properties:

parameter_dimension

Dimension \(p\) of the parameter vector \(\bfmu\) that the operator matrix depends on.

state_dimension

Dimension \(r\) of the state \(\qhat\) that the operator acts on.

Methods:

apply	Apply the operator to the given state and input at the specified parameter value, \(\Ophat_\ell(\qhat,\u;\bfmu)\).
copy	Return a copy of the operator.
evaluate	Evaluate the operator at the given parameter value, resulting in a nonparametric operator.
galerkin	Get the (Petrov-)Galerkin projection of this operator.
jacobian	Construct the state Jacobian of the operator, \(\ddqhat\Ophat_\ell(\qhat,\u;\bfmu)\).
load	Load an operator from an HDF5 file.
save	Save the operator to an HDF5 file.
verify	Verify dimension attributes and evaluate().