Non-diagonal noise support

[sho7014]

Hello,

SDEs with non-diagonal noise:
https://diffeq.sciml.ai/stable/tutorials/sde_example/#Example-4:-Systems-of-SDEs-with-Non-Diagonal-Noise
give rise to assersion error trapped at L91 of:
https://github.com/PIK-ICoNe/NetworkDynamics.jl/blob/57635388611caddabc47f7bfd64899b3aaf1f1c8/src/nd_ODE_Static.jl

I would appreciate it if you could add support or suggest a workaround.

[sho7014]

I have made some workaround.
https://github.com/sho7014/NetworkDynamics.jl
A struct NonDiagonalSDEVertex is introduced to deal with non-diagonal noise.
Both node-dependent/independent non-diagonal noise can be handled.
This is just a naive workaround, so its performance has not been examined and important features such as sparse arrays for 'noise_rate_prototype' are not supported.

[lindnemi]

Thank you for raising this issue and providing a workaround. I just returned from holiday and will look into this problem within the next weeks.

[lindnemi]

Just to clarify: Do you want "local, non-diagonal" noise at each vertex, or should noise terms at different vertices interact with each other as well?

[lindnemi]

For the first case I would suggest to construct the noise function g directly, i.e. without using network_dynamics since the whole Edge handling is then not necessary (and neither are internal states). Instead the noise matrix could directly be assembled from noise vertices.

It might then make sense to define a new constructor that directly assembles a NetworkNoise function out of the NonDiagonalSDEVertices that you defined.

[sho7014]

I would like to use the first one, hence your suggestion:

to construct the noise function g directly, i.e. without using network_dynamics since the whole Edge handling is then not necessary (and neither are internal states)

would suffice. I had a strong bias that I had to introduce a second graph layer.

[sho7014]

Should I close the issue? I am new to this kind of communities so have not yet been sure of the conventions.

[lindnemi]

I'll leave it open for now, since the issue is not entirely fixed. For once, it would be nice to have such a network_noise constructor in the package, though i don't know when i will find the time to implement it. If you want to tackle the problem and open a pull request, that would be very welcome.

On the other hand, we recommend the approach with "the second graph layer" in our tutorials when sometimes it would be more straightforward to implement g directly. So the tutorials should be expanded.

When these thing are done, i will close the issue.

[sho7014]

I agree with the idea that such network_noise constructor would be nice. I would also like to work on it when I have time.