Are there any plans to extend this to SINDY with control (SINDYc)?

[billtubbs]

Presumably I can't use PySindy 'out-of-the-box' for a problem with actuated control inputs. Or is there a way?

If not, are there any plans to extend this to SINDY with control (SINDYc)?

thanks.

[briandesilva]

There isn't a straightforward way to include actuated control inputs at the moment. SINDYc is on our roadmap, but I can make it a higher priority and implement it soon if it would be useful to you.

[briandesilva]

This is related to #40. I'm going to close issue in favor of that one and work on getting this implemented this week.

[billtubbs]

Excellent. Thanks.

[billtubbs]

If it helps, I published my own SINDy code below including examples of how to use it for systems with actuated inputs (SINDYc). As it turned out, this was quite easy to do in my case — I didn't need to change the SINDy code at all to include control inputs.

The two Jupiter notebooks show examples of identifying the Lorenz system, one without the control input and one with. Also note, these notebooks also show how to do sparse regression with existing Scikit-Learn tools. Might be interesting to investigate how Scikit-Learn does sparse feature selection and see how it differs from the SINDy method.

https://github.com/billtubbs/dyn-opt

[briandesilva]

I took a look at your repo -- I love the look of those plots!

I'm just about done with the SINDYc implementation. Well, the implementation is done, but I still need to write some unit tests and examples. It looks like we both approached it the same way; it essentially comes down to adding the control inputs without changing the left-hand side.

I agree with your observation about sklearn's feature selection. It definitely seems worth looking into.

[billtubbs]

I figured out one deficiency with scikit-learn's feature selection approach. If you try to find a sparse model for a function with more than one output variable using SelectFromModel(estimator, threshold, max_features), it comes up with a reduced set of features (inputs) that is common to all output variables. So when you do the subsequent linear regression step it may use more coefficients than it should for some variables. If that makes sense. Whereas SINDy finds a coefficient matrix.