Hi everyone, I got a new pre-print out on arXiv, that uses the Julia’s SciML ecosystem quite a bit.
The base idea is: if we consider a complex network that changes in time as a dynamical system (and take a nice model for it, such as a Random Dot Product Graphs, that gives in theory smooth trajectories) can we use SciML to recover the differential equations that guide that system?
The idea started out as a thesis project for one of my students some years ago. At that point, I was convinced the problem was easy to solve, and mostly about implementing some clever UDE code. Student worked super hard, very well, on that project, but our results were meh. I parked it for a while. Then I got back to it after some reflection, but the more I worked on it, the harder the problem showed to be, and now I’m quite convinced it’s actually not possible to solve it as is. So now it’s mostly a differential-geometry-with-some-Julia code kind of paper.
Yet, maybe I can nerd snipe some of you to come up with something super clever and fix it?