An analysis of Universal Differential Equations for data-driven discovery of Ordinary Differential Equations
This work provides an incremental analysis of Physics-informed Machine Learning frameworks, addressing challenges in data-driven scientific discovery for researchers in computational science.
The authors analyzed the Universal Differential Equations framework for discovering Ordinary Differential Equations from data, identifying issues when combining data-driven methods with numerical solvers and emphasizing the importance of data collection in two case studies.
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.