Graph neural networks have emerged as a powerful tool for large-scale mesh-based physics simulation. Existing approaches primarily employ hierarchical, multi-scale message passing to capture long-range dependencies within the graph. However, these graph hierarchies are typically fixed and manually designed, which do not adapt to the evolving dynamics present in complex physical systems. In this paper, we introduce a novel neural network named DHMP, which learns Dynamic Hierarchies for Message Passing networks through a differentiable node selection method. The key component is the anisotropic message passing mechanism, which operates at both intra-level and inter-level interactions. Unlike existing methods, it first supports directionally non-uniform aggregation of dynamic features between adjacent nodes within each graph hierarchy. Second, it determines node selection probabilities for the next hierarchy according to different physical contexts, thereby creating more flexible message shortcuts for learning remote node relations. Our experiments demonstrate the effectiveness of DHMP, achieving 22.7% improvement on average compared to recent fixed-hierarchy message passing networks across five classic physics simulation datasets.

翻译：图神经网络已成为大规模网格物理仿真的强大工具。现有方法主要采用分层、多尺度的消息传递来捕获图中的长程依赖关系。然而，这些图层次结构通常是固定且人工设计的，无法适应复杂物理系统中不断演化的动态特性。本文提出了一种名为DHMP的新型神经网络，它通过可微分的节点选择方法，学习用于消息传递网络的动态层次结构。其核心组件是各向异性消息传递机制，该机制在层级内与层级间两个层面进行交互。与现有方法不同，它首先支持在每个图层次结构内，对相邻节点间的动态特征进行方向非均匀聚合。其次，它根据不同的物理情境确定下一层级的节点选择概率，从而为学习远程节点关系创建更灵活的消息捷径。我们的实验证明了DHMP的有效性，在五个经典物理仿真数据集上，相较于近期固定层次的消息传递网络，平均性能提升了22.7%。