An analysis of Universal Differential Equations for data-driven
  discovery of Ordinary Differential Equations
Mattia Silvestri Federico Baldo Eleonora Misino Michele Lombardi
In the last decade, the scientific community has devolved its attention to
the deployment of data-driven approaches in scientific research to provide
accurate and reliable analysis of a plethora of phenomena. Most notably,
Physics-informed Neural Networks and, more recently, Universal Differential
Equations (UDEs) proved to be effective both in system integration and
identification. However, there is a lack of an in-depth analysis of the
proposed techniques. In this work, we make a contribution by testing the UDE
framework in the context of Ordinary Differential Equations (ODEs) discovery.
In our analysis, performed on two case studies, we highlight some of the issues
arising when combining data-driven approaches and numerical solvers, and we
investigate the importance of the data collection process. We believe that our
analysis represents a significant contribution in investigating the
capabilities and limitations of Physics-informed Machine Learning frameworks.