ZPDSN: spatio-temporal meteorological forecasting with topological data analysis

Meteorological forecasting is of paramount importance for safeguarding human life, mitigating natural disasters, and promoting economic development. However, achieving precise forecasts poses significant challenges owing to the complexities associated with feature representation in observed meteorological data and the dynamic spatio-temporal dependencies therein. Graph Neural Networks (GNNs) have gained prominence in addressing spatio-temporal forecasting challenges, owing to their ability to model non-Euclidean data structures and capture spatio-temporal dependencies. However, existing GNN-based methods lead to obscure of spatio-temporal patterns between nodes due to the over-smoothing problem. Worse still, important high-order structural information is lost during GNN propagation. Topological Data Analysis (TDA), a synthesis of mathematical analysis and machine learning methodologies that can mine the higher-order features present in the data itself, offers a novel perspective for addressing cross-domain spatio-temporal meteorological forecasting tasks. To leverage above problems more effectively and empower GNN with time-aware ability, a new spatio-temporal meteorological forecasting model with topological data analysis is proposed, called Zigzag Persistence with subgraph Decomposition and Supra-graph construction Network (ZPDSN), which can dynamically simulate meteorological data across the spatio-temporal domain. The adjacency matrix for the final spatial dimension is derived by treating the topological features captured via zigzag persistence as a high-order representation of the data, and by introducing subgraph decomposition and supra-graph construction mechanisms to better capture spatial-temporal correlations. ZPDSN outperforms other GNN-based models on four meteorological datasets, namely, temperature, cloud cover, humidity and surface wind component.