SINDy#

class SINDy(library, output_dimension)[source]#

Bases: Module

SINDy model class.

The Sparse Identification of Nonlinear Dynamics (SINDy) model identifies the governing equations of a dynamical system from data by learning a sparse linear combination of non-linear candidate functions.

The output of the model is expressed as product of a library matrix and a coefficient matrix:

\[\dot{X} = \Theta(X) \Xi\]
where:

  • \(X \in \mathbb{R}^{B \times D}\) is the input snapshots of the system state. Here, \(B\) is the batch size and \(D\) is the number of state variables.

  • \(\Theta(X) \in \mathbb{R}^{B \times L}\) is the library matrix obtained by evaluating a set of candidate functions on the input data. Here, \(L\) is the number of candidate functions in the library.

  • \(\Xi \in \mathbb{R}^{L \times D}\) is the learned coefficient matrix that defines the sparse model.

See also

Original reference: Brunton, S.L., Proctor, J.L., and Kutz, J.N. (2016). Discovering governing equations from data: Sparse identification of non-linear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932-3937. DOI: 10.1073/pnas.1517384113

Initialization of the SINDy class.

Parameters:

  • library (list[Callable]) – The collection of candidate functions used to construct the library matrix. Each function must accept an input tensor of shape [..., D] and return a tensor of shape [..., 1].

  • output_dimension (int) – The number of output variables, typically the number of state derivatives. It determines the number of columns in the coefficient matrix.

Raises:

  • ValueError – If library is not a list of callables.

  • AssertionError – If output_dimension is not a positive integer.

forward(x)[source]#

Forward pass of the SINDy model.

Parameters:

x (torch.Tensor) – The input batch of state variables.

Returns:

The predicted time derivatives of the state variables.

Return type:

torch.Tensor

property library#

The library of candidate functions.

Returns:

The library.

Return type:

list[Callable]

property coefficients#

The coefficients of the model.

Returns:

The coefficients.

Return type:

torch.Tensor