  Networked dynamical systems are widely used as formal models of real-world
cascading phenomena, such as the spread of diseases and information. Prior
research has addressed the problem of learning the behavior of an unknown
dynamical system when the underlying network has a single layer. In this work,
we study the learnability of dynamical systems over multilayer networks, which
are more realistic and challenging. First, we present an efficient PAC learning
algorithm with provable guarantees to show that the learner only requires a
small number of training examples to infer an unknown system. We further
provide a tight analysis of the Natarajan dimension which measures the model
complexity. Asymptotically, our bound on the Nararajan dimension is tight for
almost all multilayer graphs. The techniques and insights from our work provide
the theoretical foundations for future investigations of learning problems for
multilayer dynamical systems.
