  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.
