关键词: 等变图神经网络, 等变性, 光滑粒子动力学, 流体粒子, 流动预测

Abstract: In recent years, Graph Neural Network (GNN) have been widely applied to complex fluid system predictions due to the ability to effectively handle structured grids and strong compositional generalization capabilities. However, from a Lagrangian mesh-free perspective, unpredictable output issues have arisen when fluid particle information, transformed through translation, rotation, or reflection, was fed into GNN. To address this problem, a prediction method based on the Equivariant Graph Neural Network-based Simulator (EGNS) was proposed. Geometric vectors were first converted into relative equivariant quantities. Then, equivariant message passing was employed at each step to ensure that the entire neural network maintained equivariance, aligning network outputs with spatial transformations of the input equivariant variables. Finally, the optimized EGNS model was trained using particle trajectories simulated by the Smoothed Particle Hydrodynamics (SPH) method. Experimental results on public fluid simulation datasets demonstrated that EGNS exhibited strong predictive performance. Compared to the Graph Neural Network-based Simulator (GNS), EGNS achieved greater accuracy in predicting fluid particle movement, velocity, and typical details, improving prediction precision by 16%.

Key words: equivariant graph neural network, equivariance, smoothed particle hydrodynamics, fluid particle, flow prediction