Graph neural networks to learn meshfree snow simulations

Abstract

Snow is a natural hazard to human life and infrastructure. This motivates current research efforts to understand the granular material. The material point method models snow as a continuum. Application length scales range from the microstructural level to full scale avalanches. This conventional numerical method relies on solely spatially local information to make local updates. The recent graph neural network machine learning model is shown to include both local and global information in making local updates. This model’s promising attribute motivates its use to replace the conventional snow simulation method. However, it is uncertain if current graph neural network applications to learn physical simulations truly learn the underlying physics. This work is inspired by the finite element community's patch-test proposed in the 1960s. This insight is used to reimagine the means a graph neural network model is evaluated. Through this novel evaluation choice, may the model be investigated on the core properties of numerical methods. Further, a state-of-the-art graph neural network model is improved to utilize unnormalized features and targets in making stable predictions. Future research recommends these machine learning models in this application make architecture design choices such that the core properties of conventional numerical methods are met.