I have figured out how to fit functions defined by arrays of number using a Basis defined with ModelToolkit.jl and DataDrivenDiffEq.jl. However, I still do not understand the use of @parameters. I initially thought that it would allow me to parameterize the basis functions, but I do not think that is the case.
My question is whether it would be possible to define a basis function to be sin(p*u) and run a variant of SINDY that would not only fit the function to the basis function but also provide a best estimate of p. This would require coupling SINDY with a neural net optimizer. Has anybody done this?
Thanks!
Gordon
It always provides and estimate of p. Remind me in a few days and we’ll have a new tutorial up that highlights this. The new deployment machine just isn’t working right now.
Hi @ChrisRackauckas ,
Consider yourself reminded :-), concerning parameter estimation. See last 2-3 messages. Cheers,
Gordon
IIUC this is shown in Automatically Discover Missing Physics by Embedding Machine Learning into Differential Equations · Overview of Julia's SciML, showing how to use the result and change parameters etc. If there’s anything more you’d like to see in the post analysis we can probably add it there.
We probably need some more docs on this (note @Julius_Martensen).
The other examples from the paper are coming to the SciMLSensitivity docs rather soon.