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).
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Allow inclusion of true zeroes in the simulation data #3
When the state x is reconstructed from the delay coordinates v after simulation, the cross-diagonal averages of a Hankel matrix need to be computed. The current function "spdiags" for doing this does not allow for true zeroes to occur in the simulation which may be problematic for certain types of data/systems. To avoid this issue, we either need to rewrite the code without the use of "spdiags", or simply add very small constants (say 1e-12) to the zero data points from the simulation.
We can also continue using the edges of the Hankel matrix for reconstruction, but this may be less accurate.
When the state x is reconstructed from the delay coordinates v after simulation, the cross-diagonal averages of a Hankel matrix need to be computed. The current function "spdiags" for doing this does not allow for true zeroes to occur in the simulation which may be problematic for certain types of data/systems. To avoid this issue, we either need to rewrite the code without the use of "spdiags", or simply add very small constants (say 1e-12) to the zero data points from the simulation.
We can also continue using the edges of the Hankel matrix for reconstruction, but this may be less accurate.