Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs

Abstract

Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three fundamental limitations. (i) Discrete neural architectures: Interlacing individually parameterized spatial and temporal blocks to encode rich underlying patterns leads to discontinuous latent state trajectories and higher forecasting numerical errors. (ii) High complexity: Discrete approaches complicate models with dedicated designs and redundant parameters, leading to higher computational and memory overheads. (iii) Reliance on graph priors: Relying on predefined static graph structures limits their effectiveness and practicability in real-world applications. In this paper, we address all the above limitations by proposing a continuous model to forecast $\text{M}$ultivariate $\text{T}$ime series with dynamic $\text{G}$raph neural $\text{O}$rdinary $\text{D}$ifferential $\text{E}$quations ($\text{MTGODE}$). Specifically, we first abstract multivariate time series into dynamic graphs with time-evolving node features and unknown graph structures. Then, we design and solve a neural ODE to complement missing graph topologies and unify both spatial and temporal message passing, allowing deeper graph propagation and fine-grained temporal information aggregation to characterize stable and precise latent spatial-temporal dynamics. Our experiments demonstrate the superiorities of $\text{MTGODE}$ from various perspectives on five time series benchmark datasets.

14 pages, 6 figures, 5 tables

References in corpus (3)

• Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling
• Simplifying Graph Convolutional Networks
• Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting

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