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.

翻译：多变时间序列预报长期以来在现实应用中受到高度重视,例如能源消耗和流量预测。虽然最近的方法显示良好的预测能力,但它们有三个基本局限性。 (一) 分光神经结构: 将单个参数化的空间和时间区块内分解成丰富的基本模式,导致不连续的潜在状态轨迹和较高的预测数字错误。 (二) 高度复杂: 分层方法使带有专用设计和冗余参数的模型复杂化,导致更高的计算和记忆图前端数据。 (三) 依赖预定义的静态结构,限制了它们的有效性和实用性。 (三) 在本文中,我们通过提出一个持续模型来预测$\ textbf{M} $Uncialtical 参数来应对所有上述限制。 以动态 $\ textbf{T}}G}$Uncialtistration系列, 上层/trolebleflical trial f} 和下层图中, 数字时间序列,不显示美元和数级阵列。