Collocation based training of neural ordinary differential equations

Abstract

The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs a..