Machine Learning-based interaction network recovery in dynamical systems

Abstract

The study of interacting dynamical systems has been a topic of continuing research interest in various fields of science and engineering. In a collection of interacting agents, the interaction network contains information about which agent interacts with which other agents. In this thesis, given the information about the dynamics of agents, we use the graph neural network-based variational auto-encoder framework to recover the interaction network underlying the dynamical system and learn its dynamics. This is done entirely from observational data in a self-supervised manner. We apply our model to two physical systems: the particles interacting via Hooke's law and the other interacting phase oscillators in the well-studied Kuramoto model. We also extend the applicability of this framework by applying it to the coupled system of financial instruments like stocks. It is well known that the log returns of several stocks are coupled with one another. Overall, we achieved an accuracy of greater than 89% in recovering the interaction matrix on all the tasks involving 5 interacting agents.