DerivativeEstimatorTemplate

class DerivativeEstimatorTemplate(time_domain)

Template for time derivative estimators.

Operator Inference for time-continuous (semi-discrete) models requires state snapshots and their time derivatives in order to learn operator entries via regression. This class is a template for estimating the first time derivative of state snapshots. Specifically, from a collection of snapshots \(\qhat_0,\ldots,\qhat_{k-1}\in\RR^r\) representing the state at time instances \(t_0,\ldots,t_{k-1}\), the goal is to estimate

\[\dot{\qhat}_j \approx \ddt\qhat(t)\bigg|_{t = t_j} \in \RR^{r}\]

for \(j = 0, \ldots, k - 1\).

Depending on the estimation strategy, the derivatives may only be computed for a subset of the states. For example, a first-order backward difference may omit an estimate for \(\dot{\qhat}_0\).

Parameters:

time_domain(k,) ndarray

Time domain of the snapshot data.

Properties:

time_domain

Time domain of the snapshot data, a (k,) ndarray.

Methods:

estimate	Estimate the first time derivatives of the states.
verify	Verify that estimate() is consistent in the sense that the all outputs have the same number of columns and test the accuracy of the results on a few test problems.
verify_shapes	Verify that estimate() is consistent in the sense that the all outputs have the same number of columns.