Local Identifiability of Networks with Nonlinear Node Dynamics

Abstract

We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear functions at the node level are known, and we aim to identify the weight matrix of the graph. Our main result is that, for almost all static analytic nonlinearities that cross the origin, directed graphs are generically locally identifiable if and only if at least one node is excited in every source component of the condensation graph and at least one node is measured in every sink component. This holds even when all other nodes remain unexcited and unmeasured and stands in sharp contrast to most findings on network identifiability requiring measurement and/or excitation of each node. The result applies to homogeneous feed-forward and recurrent artificial neural networks and generalizes previous literature by considering a broader class of activations and architectures.