Basis Learning for Dynamical Systems in the Presence of Incomplete Scientific Knowledge

Knowledge discovery researchers have recently made great progress on techniques to learn the governing equations of dynamic systems from system data. However, many of these techniques rely on significant prior knowledge about the system in question. One strong assumption is that researchers know a basis for the vector space the governing equations are in. In this paper we propose a technique to learn a set of functions that form a complete basis when only some of the basis functions are known beforehand by the researcher. We then empirically demonstrate our technique on real dynamical systems and show it is effective in learning a basis for the vector space that the governing equations are contained in.