Machine learning methods for physical simulation have achieved significant
success in recent years. We propose a new universal architecture based on Graph
Neural Network, the Message Passing Transformer, which incorporates a Message
Passing framework, employs an Encoder-Processor-Decoder structure, and applies
Graph Fourier Loss as loss function for model optimization. To take advantage
of the past message passing state information, we propose Hadamard-Product
Attention to update the node attribute in the Processor, Hadamard-Product
Attention is a variant of Dot-Product Attention that focuses on more
fine-grained semantics and emphasizes on assigning attention weights over each
feature dimension rather than each position in the sequence relative to others.
We further introduce Graph Fourier Loss (GFL) to balance high-energy and
low-energy components. To improve time performance, we precompute the graph's
Laplacian eigenvectors before the training process. Our architecture achieves
significant accuracy improvements in long-term rollouts for both Lagrangian and
Eulerian dynamical systems over current methods.

基于图神经网络的新型智能体架构 —— 消息传递变换器，结合了消息传递框架，采用了编码器 - 处理器 - 解码器结构，以及应用了图傅里叶损失作为模型优化的损失函数。