Learning ODE Models with Qualitative Structure Using Gaussian Processes

Recently there has been increasing interest in the use of learning techniques to model dynamical systems directly from data for scientific and engineering applications. However, in many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be practicable. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain-specific knowledge. We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points. We show that this combination improves extrapolation and long-term behaviour, and reduces computational cost.