Network Inference from Heat Diffusion Dynamics

We address the problem of network connectivity inference by observing interacting time-series signals at the nodes. The evolving nodal signals depend on the connectivity structure of the network thus allowing us to successfully invert for it. Our approach is demonstrated using the example of heat diffusion dynamics. To learn the graph, we combine our knowledge of the dynamical equation and the observed graph signals. Specifically, we perform approximate numerical discretization of the dynamical equation leading to a system of linear equations in the unknown graph topology. Simulations indicate feasibility of this method for accurate network inference.