This is a testbed for system identification and forecasting of dynamical systems using the Hankel Alternative View of Koopman (HAVOK) algorithm and Sparse Identification of Nonlinear Dynamics (SINDy). This code is based on the work by Brunton & Kutz (2022) and Yang et. al. (2022).
The SINDy algorithm can be used to find a linear (HAVOK) representation in nonlinear measurement coordinates. Basically, the delay-embedded function space, v, is augmented with additional nonlinear functions of the delay variables; v_1^2, sin(v_1), v_1*v_2, etc.
This adds additional computational effort but may allow for a better representation when the HAVOK rank is low. This may also provide a better representation than simply building a model using SINDy on the measurement functions; x, x^2, sin(x), etc.
The SINDy algorithm can be used to find a linear (HAVOK) representation in nonlinear measurement coordinates. Basically, the delay-embedded function space, v, is augmented with additional nonlinear functions of the delay variables; v_1^2, sin(v_1), v_1*v_2, etc.
This adds additional computational effort but may allow for a better representation when the HAVOK rank is low. This may also provide a better representation than simply building a model using SINDy on the measurement functions; x, x^2, sin(x), etc.