Learning Dynamical Systems with Side Information (short version)

We present a mathematical formalism and a computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information (e.g., physical laws or contextual knowledge). We identify six classes of side information which can be imposed by semidefinite programming and that arise naturally in many applications. We demonstrate their value on two examples from epidemiology and physics. Some density results on polynomial dynamical systems that either exactly or approximately satisfy side information are also presented.