Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations, rotations, etc, leading to better generalization ability. Nevertheless, their frame-to-frame formulation of the task overlooks the non-Markov property mainly incurred by unobserved dynamics in the environment. In this paper, we reformulate dynamics simulation as a spatio-temporal prediction task, by employing the trajectory in the past period to recover the Non-Markovian interactions. We propose Equivariant Spatio-Temporal Attentive Graph Networks (ESTAG), an equivariant version of spatio-temporal GNNs, to fulfill our purpose. At its core, we design a novel Equivariant Discrete Fourier Transform (EDFT) to extract periodic patterns from the history frames, and then construct an Equivariant Spatial Module (ESM) to accomplish spatial message passing, and an Equivariant Temporal Module (ETM) with the forward attention and equivariant pooling mechanisms to aggregate temporal message. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level. Experimental results verify the effectiveness of ESTAG compared to typical spatio-temporal GNNs and equivariant GNNs.

翻译：学习表示和模拟物理系统的动力学是一项关键但具有挑战性的任务。现有的基于等变图神经网络（GNN）的方法囊括了物理对称性（例如平移、旋转等），从而实现了更好的泛化能力。然而，这些方法采用帧到帧的任务形式化，忽略了主要由环境中不可观测动力学导致的非马尔可夫性质。本文通过利用历史时间段内的轨迹恢复非马尔可夫相互作用，将动力学模拟重新形式化为一个时空预测任务。我们提出等变时空注意力图网络（ESTAG），一种等变版本的时空GNN，以实现上述目标。其核心在于，我们设计了一种新颖的等变离散傅里叶变换（EDFT），用于从历史帧中提取周期模式，进而构建等变空间模块（ESM）实现空间消息传递，以及带有前向注意力和等变池化机制的等变时间模块（ETM）聚合时间消息。我们在对应于分子、蛋白质和宏观层面的三个真实数据集上评估了模型。实验结果验证了ESTAG相较于典型时空GNN和等变GNN的有效性。