Exploring the missing values is an essential but challenging issue due to the
complex latent spatio-temporal correlation and dynamic nature of time series.
Owing to the outstanding performance in dealing with structure learning
potentials, Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs)
are often used to capture such complex spatio-temporal features in multivariate
time series. However, these data-driven models often fail to capture the
essential spatio-temporal relationships when significant signal corruption
occurs. Additionally, calculating the high-order neighbor nodes in these models
is of high computational complexity. To address these problems, we propose a
novel higher-order spatio-temporal physics-incorporated GNN (HSPGNN). Firstly,
the dynamic Laplacian matrix can be obtained by the spatial attention
mechanism. Then, the generic inhomogeneous partial differential equation (PDE)
of physical dynamic systems is used to construct the dynamic higher-order
spatio-temporal GNN to obtain the missing time series values. Moreover, we
estimate the missing impact by Normalizing Flows (NF) to evaluate the
importance of each node in the graph for better explainability. Experimental
results on four benchmark datasets demonstrate the effectiveness of HSPGNN and
the superior performance when combining various order neighbor nodes. Also,
graph-like optical flow, dynamic graphs, and missing impact can be obtained
naturally by HSPGNN, which provides better dynamic analysis and explanation
than traditional data-driven models. Our code is available at
this https URL

通过融合动态的高阶空时 GN，通过使用空间注意机制生成动态拉普拉斯矩阵，并使用物理动态系统的普遍非齐次偏微分方程来构建高阶空时 GN，以获得缺失的时间序列值，并通过归一化流来评估图中每个节点的重要性从而更好地解释缺失的影响。