Creating ODESystems for HAVOK

[whpowell96]

Right now ODESystem works great for making ODE system and then an ODEProblem from the basis coming out of the SINDy sparse regression, but with HAVOK, one of the variables in the regression is either used as forcing or is estimated via some sort of convolution. Right now ODESystem does not seem to be able to create these sort of systems and it seems like the only way to construct an appropriate ODE system for a HAVOK model is to manually extract the matrix and from the SINDy basis and fit a spline to the forcing mode and create your own ODE function from that. It is possible there is something I am missing since the docs currenty 404.

My 2 main questions are

1. Is there anyway to generate ODE functions for HAVOK models useing ODESystem by a different specification of the SINDy problem or something else?

2. Is there a better way of extracting the matrix from the SINDy output basis regressed on a linear basis?

[AlCap23]

I am thinking about this ( and also see #56 ). Currently my target is to write up the docs, get some additional optimisation / identification routines for SINDY running and then get to the delays.
The implementation of HAVOK ( at least what is in the examples, there is a different PR open for this #53 ) is rather experimental.

To answer your questions:

1. Not yet

2. Maybe you can try sparse_regression defined here. There is also an iip version which gives you the matrix given DX and Theta, which should be the delay stuff)

Hope this helps.

[whpowell96]

Hi, this helped a lot. I think that the best way to go forward with this would be usign sparse_regression and manually creating an ODE system, which isn't that hard if you are using v_{r+1} as a forcing function since you can just use some interpolation package, but doing actual online prediction using HAVOK where v_{r+1} is being estimated by convolving with left singular vectors is likely more involved. I look forward to seeing what features get added to this package.

[AlCap23]

I'll close this for now :)