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

深度学习中的长期多变量时间序列预测(LMTF)模型的研究进展表明，基于历史数值和基于时间索引的模型在处理多变量时间序列时能更准确地预测未来值，而本文介绍的PDETime模型在实验中表现出优异的适应性和最先进的结果

PDETime：从偏微分方程角度重新思考长期多元时间序列预测