The majority of real-world processes are spatiotemporal, and the data generated by them exhibits both spatial and temporal evolution. Weather is one of the most essential processes in this domain, and weather forecasting has become a crucial part of our daily routine. Weather data analysis is considered the most complex and challenging task. Although numerical weather prediction models are currently state-of-the-art, they are resource-intensive and time-consuming. Numerous studies have proposed time series-based models as a viable alternative to numerical forecasts. Recent research in the area of time series analysis indicates significant advancements, particularly regarding the use of state-space-based models (white box) and, more recently, the integration of machine learning and deep neural network-based models (black box). The most famous examples of such models are RNNs and transformers. These models have demonstrated remarkable results in the field of time-series analysis and have demonstrated effectiveness in modelling temporal correlations. It is crucial to capture both temporal and spatial correlations for a spatiotemporal process, as the values at nearby locations and time affect the values of a spatiotemporal process at a specific point. This self-contained paper explores various regional data-driven weather forecasting methods, i.e., forecasting over multiple latitude-longitude points (matrix-shaped spatial grid) to capture spatiotemporal correlations. The results showed that spatiotemporal prediction models reduced computational costs while improving accuracy. In particular, the proposed tensor train dynamic mode decomposition-based forecasting model has comparable accuracy to the state-of-the-art models without the need for training. We provide convincing numerical experiments to show that the proposed approach is practical.

翻译：现实世界中的大多数过程都具有时空特性，其生成的数据同时呈现空间和时间演化规律。天气预报是该领域最核心的过程之一，已成为日常生活中的重要组成部分。气象数据分析被认为是最复杂且最具挑战性的任务。尽管数值天气预报模型目前处于最前沿水平，但其资源消耗大且计算耗时。大量研究提出基于时间序列的模型作为数值预报的可行替代方案。近年来时间序列分析领域的研究表明，特别是基于状态空间的白箱模型，以及近期融合机器学习与深度神经网络的黑箱模型取得了显著进展。最典型的例子包括RNN和Transformer模型。这些模型在时间序列分析领域展现出卓越效果，并已证明能够有效建模时间相关性。对于时空过程而言，同时捕捉时间与空间相关性至关重要，因为邻近位置和时刻的数值会影响该过程在特定点的取值。本文作为独立研究，探讨了多种区域数据驱动的天气预报方法，即通过多经纬度点（矩阵形式空间网格）的联合预测来捕捉时空相关性。结果表明，时空预测模型在提升精度的同时降低了计算成本。特别地，我们提出的基于张量列动态模式分解的预测模型无需训练即可达到与最先进模型相当的精度。我们通过具有说服力的数值实验证明了该方法的实用性。