Feature Request: Jacobian along Trajectory

[jClugstor]

I think it would be very good if we were able to calculate the jacobian of the system along the trajectory. Among other advantages, this would allow us to find the lyapunov exponent spectrum of the attractor. Is this a possibility? I would be willing to help with this in anyway possible, if this is feasible.

[MartinuzziFrancesco]

This is very doable, it just needs the esn to be a callable function of the input esn(x) and call the jacobian from ForwadDiff. This will need a little re arranging of the internals and also some API calls, but I think this is long overdue. I'll write a high level post under this issue detailing the changes and we can split some of the work if you want

[jClugstor]

Sorry for waiting so long to reply, that sounds great to me!

[jClugstor]

Any updates on this? The semester is finally over, so I'll have a lot of time to help for a couple of months.

[MartinuzziFrancesco]

Sorry it took me a while to get back at you, I initially thought that the solution would have involved a little more foundation work but I think that there is a quick solution. In order to get the Jacobian we would need a model that inputs and outputs a vector, that at the moment we don't have since the esn and the output_layer are not in the same struct. I think it would suffice the have a build_model function that takes as input the ESN struct and the output_layer struct and return a single function based on a mutable struct that also recursively saves the reservoir state for each input. I can get some starting code done later this week if you think this description feels convoluted

[jClugstor]

I think I see what you're getting at, but I'll be on vacation for the next two weeks so I won't have much of a chance to look at it. When I get back though I can definitely take a look.

[jClugstor]

Alright, so I think what you're saying is that there could be some function like
function build_model(esn::ESN, opl::OutputLayer) . . end
that should return a function that will take a vector, and output the next prediction?

[MartinuzziFrancesco]

yes, that is more or less what is on my mind!