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.

本文提出了一种使用动态图神经普通微分方程（MTGODE）来预测多元时间序列的连续模型，旨在解决离散神经网络在捕捉稳定和精确的时空动态时所遇到的困难。我们的实验证明了该方法从多种角度在五个时间序列基准数据集上的超越性。