Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs

TL;DR

This paper introduces MTGODE, a continuous neural ODE-based model for multivariate time series forecasting that dynamically learns graph structures, overcoming limitations of discrete architectures and static priors, leading to improved accuracy and efficiency.

Contribution

The paper proposes a novel neural ODE framework for multivariate time series forecasting that models dynamic graphs and unifies spatial-temporal message passing, addressing key limitations of existing methods.

Findings

Outperforms existing methods on five benchmark datasets.

Effectively models dynamic graph structures and temporal evolution.

Achieves deeper graph propagation and more accurate latent dynamics.

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 $\textbf{M}$ultivariate $\textbf{T}$ime series with dynamic $\textbf{G}$raph neural $\textbf{O}$rdinary $\textbf{D}$ifferential $\textbf{E}$quations ($\texttt{MTGODE}$). 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 $\texttt{MTGODE}$ from various perspectives on five time series benchmark datasets.