Multi-grid graph neural networks with self-attention for computational mechanics

Combining computational mechanics with machine learning has recently attracted a lot of attention, especially in computational mechanics, where researchers aim to improve the accuracy and computational cost of the simulations. While convolutional neural networks have been used to turn mesh data into images, newer methods now use graph neural networks to work directly with mesh structures. In this work, we introduce a new multigrid graph neural network framework, designed for time-dependent three-dimensional computational fluid dynamics simulations. The proposed method uses self-attention within the message-passing steps to better understand the solution behavior across both space and time. It also uses attention scores to dynamically prune and refine meshes, making it possible to handle large-scale simulations efficiently without losing accuracy. Inspired by Bidirectional Encoder (BERT), we also add a self-supervised training method tailored for graphs, which helps the model generalize better. Tests on benchmark datasets show that the method performs better than current state-of-the-art approaches, even on larger and more complex meshes. Codes and datasets are available at https://github.com/DonsetPG/graph-physics.