Spatiotemporal prediction in three-dimensional space by separating information interactions

Spatiotemporal prediction in two-dimensional (2D) space has been widely studied in computer science and geosciences, such as video prediction and weather forecasting. However, many spatiotemporal evolutions take place in three-dimensional (3D) space, e.g., atmospheric temperature changes of multiple isobaric surfaces. For such a 3D multi-plane prediction task, existing methods usually fail to model the information interactions between different 2D planes. In this paper, we propose a novel neural network-based method to tackle 3D multi-plane spatiotemporal prediction tasks. Specifically, compared with prediction in 2D space, information interactions in 3D space are more complicated because of the emergence of a new dimension. To clarify these interactions, we first propose to separate them into three types, i.e., inter-level interaction, intralevel interaction, and unknown residual interaction. This separation is novel and comprehensive, which covers vertical, horizontal, and potentially unknown factors. Based on the separation, we design a new spatiotemporal module for prediction. It contains three units to capture the three separated interactions, respectively: (1) an inter-level interaction unit, which is the first one dedicated to modeling the information interaction between different levels. The inter-level interaction, as a new feature in 3D space, has not been effectively studied. Hence, in this unit, we propose to model it by leveraging the spatial associations between adjacent levels and developing a new dynamics simulation. (2) An infra-level interaction unit is utilized to model the information interaction within the same level. With the benefit of interaction separation, we can leverage the neural partial differential equations to formulate spatiotemporal dynamics and exploit prior physical knowledge in data. (3) Furthermore, a residual unit is employed to capture the remaining unknown and uncertain factors, which can help further improve the expressiveness of our model. As for a prediction, we employ the three units to capture various dynamics, and combine them to obtain a comprehensive one. The final dynamics will be decoded for generating prediction via a convolutional neural network. We conduct extensive experiments on a dataset of atmospheric temperature changes. The experimental results show that our method obtains a significant improvement and achieves a new state-of-the-art performance.