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Bayesian Sparse Identification of Nonlinear Dynamics (Bayesian-SINDy)

Model discovery from data for nonlinear dynamical systems using type-II maximum likelihood in the Bayesian statistics, i.e. maximising evidence (or marginal likelihood).

Derived from the original SINDy paper "Discovering governing equations from data: Sparse identification of nonlinear dynamical systems" in the Proceedings of the National Academy of Sciences, 113(15):3932-3937, 2016, by S. L. Brunton, J. L. Proctor, and J. N. Kutz.

This code is part of this article by L. Fung, U. Fasel and M. P. Juniper.

Using the code

Getting started (without SparseBayes )

  1. Run one of the .m script in MATLAB at the top level folder and start exploring!

(Optional) To run SparseBayes for comparison

  1. Download the SparseBayes package here
  2. Unzip the folder and place it in this current folder.
  3. Run one of the .m script at the top level folder.

Note on dependency and license

This code is derived from the original code on SINDy by Brunton, Proctor & Kutz (2016, PNAS). Some of the files (namely, SparseGalerkin.m, poolData.m, poolDataList.m and sparsifyDynamics.m) are directly copied from the original SINDy work, under the permission of the original authors. Please refer to the specific files or LICENSE to see the full attribution.

Comparison with SparseBayes is also included in the code. To respect the licensing of their code, these files are not included in this repo. To run those part of the code, please download them from their web page according to the instructions above.