On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods
This is an incremental survey that aims to bridge gaps between machine learning and computational science for researchers in both fields.
The paper surveys parallels between graph neural networks for physical system simulation and classical numerical methods, identifying untapped simulation approaches that could improve the accuracy and efficiency of machine learning models in scientific applications.
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 with the parallels between the development trajectories of graph neural network acceleration for physical simulations and 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 make 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.