fit()

fit()#

DiscreteModel.fit(states, nextstates=None, inputs=None)[source]#

Learn the model operators from data.

The operators are inferred by solving the regression problem

\[\min_{\Ohat}\sum_{j=0}^{k-1}\left\| \fhat(\qhat_j, \u_j) - \zhat_{j} \right\|_2^2 = \min_{\Ohat}\left\| \D\Ohat\trp - [~\zhat_0~~\cdots~~\zhat_{k-1}~]\trp \right\|_F^2\]

where \(\zhat_j = \fhat(\qhat_j, \u_j)\) is the model and

  • \(\qhat_j\in\RR^r\) is a measurement of the state,

  • \(\u_j\in\RR^m\) is a measurement of the input, and

  • \(\zhat_j\in\RR^r\) is a measurement of the next state iteration after \(\qhat_j\),

  • \(\Ohat\in\RR^{r\times d(r,m)}\) is the operator matrix such that \(\fhat(\q,\u) = \Ohat\d(\qhat,\u)\) for some data vector \(\d(\qhat,\u)\in\RR^{d(r,m)}\), and

  • \(\D\in\RR^{k\times d(r,m)}\) is the data matrix given by \([~\d(\qhat_0,\u_0)~~\cdots~~\d(\qhat_{k-1},\u_{k-1})~]\trp\),

See the opinf.operators module for further explanation.

The strategy for solving the regression, as well as any additional regularization or constraints, are specified by the solver.

Parameters:
states(r, k) ndarray

Snapshot training data. Each column is a single snapshot.

nextstates(r, k) ndarray or None

Next iteration training data. Each column nextstates[:, j] is the iteration following states[:, j]. If None, use nextstates[:, j] = states[:, j+1].

inputs(m, k) or (k,) ndarray or None

Input training data. Each column inputs[:, j] corresponds to the snapshot states[:, j]. May be a one-dimensional array if m=1 (scalar input).

Returns:
self
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