autokoopman.estimator package

Submodules

autokoopman.estimator.dmd module

class autokoopman.estimator.dmd.DMDEstimator(normalize=True, feature_range=(-1, 1), weights=None)

Bases: NextStepEstimator

fit_next_step(X: ndarray, Y: ndarray) → None

an alternative fit method that uses a trajectories data structure

property model: System

class autokoopman.estimator.dmd.MultiDMD(svd_rank=0, tlsq_rank=0, exact=False, opt=False, rescale_mode=None, forward_backward=False, sorted_eigs=False, tikhonov_regularization=None)

Bases: DMD

fit_multi(X, Y)

Compute the Dynamic Modes Decomposition to the input data. :param X: the input snapshots. :type X: numpy.ndarray or iterable

autokoopman.estimator.koopman module

class autokoopman.estimator.koopman.KoopmanContinuousEstimator(observables, dim, rank, weights=None, **kwargs)

Bases: GradientEstimator

Koopman Continuous Estimator

Parameters:

• observables – function that returns the observables of the system state

• dim – dimension of the system state

• rank – rank of the DMDc

• weights – observation weights (optional)

References

Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2018). Generalizing Koopman theory to allow for inputs and control. SIAM Journal on Applied Dynamical Systems, 17(1), 909-930.

See https://epubs.siam.org/doi/pdf/10.1137/16M1062296 for more details

fit_gradient(X: ndarray, Y: ndarray, U: ndarray | None = None, weights: ndarray | None = None) → None

fits the gradient system model

calls DMDC after building out the observables

property model: System

packs the learned linear transform into a continuous linear system

class autokoopman.estimator.koopman.KoopmanDiscEstimator(observables, sampling_period, dim, rank, weights=None, **kwargs)

Bases: NextStepEstimator

Koopman Discrete Estimator

This methods implements a regularized form of Koopman with Inputs (KIC). It assumes that the input if piecewise constant, zeroing out some of the state + input transform.

TODO: add other ways to implement KIC TODO: sampling period isn’t used

Parameters:

• observables – function that returns the observables of the system state

• sampling_period – sampling period of the uniform time, discrete system

• dim – dimension of the system state

• rank – rank of the DMDc

• weights – observation weights (optional)

References

Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2018). Generalizing Koopman theory to allow for inputs and control. SIAM Journal on Applied Dynamical Systems, 17(1), 909-930.

See https://epubs.siam.org/doi/pdf/10.1137/16M1062296 for more details

fit_next_step(X: ndarray, Y: ndarray, U: ndarray | None = None, weights: ndarray | None = None) → None

fits the discrete system model

calls DMDC after building out the observables

property model: System

packs the learned linear transform into a discrete linear system

autokoopman.estimator.koopman.dmdc(X, Xp, U, r)

Dynamic Mode Decomposition with Control (DMDC)

DMD but extended to include control.

References

Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2016). Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems, 15(1), 142-161.

See https://arxiv.org/pdf/1409.6358.pdf for more details

autokoopman.estimator.koopman.swdmdc(X, Xp, U, r, Js, W)

State Weighted Dynamic Mode Decomposition with Control (wDMDC)

autokoopman.estimator.koopman.wdmdc(X, Xp, U, r, W)

Weighted Dynamic Mode Decomposition with Control (wDMDC)

autokoopman.estimator.sindy module

Module contents