Multivariate Time Series Forecasting With Dynamic Graph Neural ODEs

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
M
ultivariate
T
ime series with dynamic
G
raph neural
O
rdinary
D
ifferential
E
quations (
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
MTGODE
from various perspectives on five time series benchmark datasets.