Learning Dynamical Systems with Side Information

We present a mathematical and computational framework for learning dynamical system from noisy observations of few trajectories subject to side information. Side information is any knowledge we might have about the would like learn, besides trajectory data, typically inferred domain-specific or basic principles scientific discipline. are interested in explicitly integrating into process order compensate scarcity observations. identify six types that arise naturally many applications lead convex constraints problem. First, show when our model unknown parameterized as polynomial, can impose computationally via semidefinite programming. then demonstrate added value dynamics models physics cell biology, well controlling epidemiology. Finally, study how polynomial systems approximate continuously differentiable ones while satisfying (either exactly approximately). Our overall methodology combines ideas optimization, real algebra, systems, functional approximation theory, potentially new synergies among these areas.