  In this paper we develop a framework to study observability for uniform
hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect
multiple nodes and unambiguously represent multi-way relationships which are
ubiquitous in many real-world networks. We extend the canonical homogeneous
polynomial or multilinear dynamical system on uniform hypergraphs to include
linear outputs, and we derive a Kalman-rank-like condition for assessing the
local weak observability. We propose an exact techniques for determining the
local observability criterion, and we propose a greedy heuristic to determine
the minimum set of observable nodes. Numerical experiments demonstrate our
approach on several hypergraph topologies and a hypergraph representations of
neural networks within the mouse hypothalamus.
