Framework for identification of chaotic systems with symbolic regression
arxiv.org
arxiv.org
What they're doing here is not that. I think if I understand it correctly they're using the neural network to generate data which when symbolically regressed with PySR yield the RHS of each ODE in the system.
What's not immediately obvious is what the benefit of introducing the neural network is--does it make it faster than the "direct" naive approach?
rsfmri data comprise multiple timeseries sampled from voxels throughtout the brain. The dynamics are complex, and there have been attempts to examine it through the lens of attractors etc. I'm not an expert in chaotic analysis, but will say that most of the advances in the field of neuroscience come from innovative analytic methods. Like I said, it was my first thought, but there is a whole subfield examining brain dynamics through these lenses.
That said, another aspect of dissipative chaos is that a highly complex system like turbulence (10^28 or so atoms bouncing off each other) often can be described by an attractor that is rather low dimensional and could be modeled with a few equations. So you might have some neural signal that tools like that could make an interesting model of.