Learning solid dynamics with graph neural network

Deep learning has shown great promise in solid physic dynamic simulation. By incorporating physical laws, recent works have further improved performance. However, existing methods rarely conform to macrophysics and incur computational costs. Furthermore, the velocity direction features of the current model have not been decomposed, forcing the model to learn vector operations. To address the aforementioned problems, we propose a Solid-Graph Network (Solid-GN), designed for more accurate and efficient learning of solid dynamics. Firstly, we design a novel and cost-effective symmetric direction encoding system that achieves macroscopic equivariance in 2D space by representing same relative directional relationships among particle pairs and their flipping version. Secondly, we propose a message-passing mechanism incorporated with the contact process, facilitating an accurate description of interactions through the decomposition of normal and tangential effects. Lastly, four novel datasets for solid dynamics with non-uniform radius particles are released, thereby enabling more complex and realistic physical simulations. Experimental evaluations conducted on five datasets demonstrate our model's performance concerning predictive accuracy, macroscopic equivariance, and computational cost over the state-of-the-art ones.