class SINDy

class deeptime.sindy.SINDy(library=None, optimizer=None, input_features=None)

Learn a dynamical systems model for measurement data using the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method.

For given measurement data \(X\), and a set of library functions evaluated on \(X\)

\[\Theta(X) = [\theta_1(X), \theta_2(X), \dots, \theta_k(X)], \]

SINDy seeks a sparse set of coefficients \(\Xi\) which satisfies

\[\dot{X} \approx \Theta(X)\Xi. \]

The i-th column of this matrix equation gives a differential equation for the i-th measurement variable (i-th column in \(X\)). For more details see [1].

Parameters:

• library (library object, optional, default=None) – The candidate feature library, \(\Theta\). The object should implement a fit(), transform(), and get_feature_names_out() methods. It should also have n_input_features_ and n_output_features_ attributes. By default a polynomial library of degree 2 is used.

• optimizer (optimizer object, optional, default=None) – The optimization routine used to solve the objective \(\dot{X} \approx \Theta(X)\Xi\). The object should have fit() and predict() methods and coef_ and intercept_ attributes. For example, any linear regressor from sklearn.linear_model should work. By default, STLSQ() is used.

• input_features (list of strings, optional, default=None) – List of input feature names. By default, the names “x0”, “x1”, …, “x{n_input_features}” is used.

References

[1]

Steven L Brunton, Joshua L Proctor, and J Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the national academy of sciences, 113(15):3932–3937, 2016.

Attributes

has_model	Property reporting whether this estimator contains an estimated model.
model	Shortcut to fetch_model().

Methods

fetch_model()	Yields the latest model.
fit(x[, y, t])	Fit the estimator to measurement data.
fit_fetch(data, **kwargs)	Fits the internal model on data and subsequently fetches it in one call.
get_params([deep])	Get the parameters.
set_params(**params)	Set the parameters of this estimator.

fetch_model() → Optional[SINDyModel]

Yields the latest model.

Returns:

model – The model.

Return type:

SINDyModel or None

fit(x, y=None, t=None)

Fit the estimator to measurement data.

Parameters:

• x (np.ndarray, shape (n_samples, n_input_features)) – Training/measurement data. Each row should correspond to one example and each column to a feature.

• y (np.ndarray, shape (n_samples, n_input_features), optional, default=None) – Array of derivatives of x. By default, np.gradient is used to compute the derivatives.

• t (np.ndarray, shape (n_samples,) or a scalar, optional, default=None) – The times when the measurements in x were taken or the (uniform) time spacing between measurements in x. By default a timestep of 1 is assumed. This argument is ignored if y is passed.

Returns:

self – Reference to self

Return type:

SINDy

fit_fetch(data, **kwargs)

Fits the internal model on data and subsequently fetches it in one call.

Parameters:

• data (array_like) – Data that is used to fit the model.

• **kwargs – Additional arguments to fit().

Returns:

The estimated model.

Return type:

model

get_params(deep=False)

Get the parameters.

Returns:

params – Parameter names mapped to their values.

Return type:

mapping of string to any

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**params (dict) – Estimator parameters.

Returns:

self – Estimator instance.

Return type:

object

property has_model: bool

Property reporting whether this estimator contains an estimated model. This assumes that the model is initialized with None otherwise.

Type:

bool

property model

Shortcut to fetch_model().