On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey we begin by providing an example of this development with the parallels between graph neural network acceleration for physical simulations and the development of particle-based approaches. We then give an overview of simulation approaches, which have not yet found their way into state-of-the-art Machine Learning methods and hold the potential to Machine Learning approaches more accurate and more efficient. We conclude by presenting an outlook on the potential of these approaches for making Machine Learning models for science more efficient.