PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from
  the perspective of partial differential equations
Shiyi Qi Zenglin Xu Yiduo Li Liangjian Wen Qingsong Wen Qifan Wang Yuan Qi
Recent advancements in deep learning have led to the development of various
models for long-term multivariate time-series forecasting (LMTF), many of which
have shown promising results. Generally, the focus has been on
historical-value-based models, which rely on past observations to predict
future series. Notably, a new trend has emerged with time-index-based models,
offering a more nuanced understanding of the continuous dynamics underlying
time series. Unlike these two types of models that aggregate the information of
spatial domains or temporal domains, in this paper, we consider multivariate
time series as spatiotemporal data regularly sampled from a continuous
dynamical system, which can be represented by partial differential equations
(PDEs), with the spatial domain being fixed. Building on this perspective, we
present PDETime, a novel LMTF model inspired by the principles of Neural PDE
solvers, following the encoding-integration-decoding operations. Our extensive
experimentation across seven diverse real-world LMTF datasets reveals that
PDETime not only adapts effectively to the intrinsic spatiotemporal nature of
the data but also sets new benchmarks, achieving state-of-the-art results