Adaptive Graph Structure Learning Neural Rough Differential Equations for Multivariate Time Series Forecasting

Multivariate time series forecasting has extensive applications in urban computing, such as financial analysis, weather prediction, and traffic forecasting. Using graph structures to model the complex correlations among variables in time series, and leveraging graph neural networks and recurrent neural networks for temporal aggregation and spatial propagation stage, has shown promise. However, traditional methods’ graph structure node learning and discrete neural architecture are not sensitive to issues such as sudden changes, time variance, and irregular sampling often found in real-world data. To address these challenges, we propose a method called <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u>daptive <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</u>raph structure <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</u>earning neural <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u>ough <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</u>ifferential <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</u>quations (AGLRDE). Specifically, we combine dynamic and static graph structure learning to adaptively generate a more robust graph representation. Then we employ a spatio-temporal encoder-decoder based on Neural Rough Differential Equations (Neural RDE) to model spatio-temporal dependencies. Additionally, we introduce a path reconstruction loss to constrain the path generation stage. We conduct experiments on six benchmark datasets, demonstrating that our proposed method outperforms existing state-of-the-art methods. The results show that AGLRDE effectively handles aforementioned challenges, significantly improving the accuracy of multivariate time series forecasting.