Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the framework of those models is designed mainly by intuition. How to make spatiotemporal forecasting with theoretical guarantees is still a challenging issue. In this work, we tackle this problem by applying domain knowledge from the dynamical system to the framework design of deep learning models. An observer theory-guided deep learning architecture, called Spatiotemporal Observer, is designed for predictive learning of high dimensional data. The characteristics of the proposed framework are twofold: firstly, it provides the generalization error bound and convergence guarantee for spatiotemporal prediction; secondly, dynamical regularization is introduced to enable the model to learn system dynamics better during training. Further experimental results show that this framework could capture the spatiotemporal dynamics and make accurate predictions in both one-step-ahead and multi-step-ahead forecasting scenarios.

翻译：尽管基于深度学习的方法在时空预测学习中取得了巨大成功，但这些模型的框架设计主要依赖直觉。如何实现具有理论保证的时空预测仍是一个具有挑战性的问题。本研究通过将动力系统领域的领域知识应用于深度学习模型框架设计来解决该问题。我们设计了一种观测器理论指导的深度学习架构——时空观测器，用于高维数据的预测学习。该框架具有两个特点：首先，它为时空预测提供了泛化误差界和收敛性保证；其次，引入动力正则化使模型在训练过程中能更好地学习系统动力学。进一步的实验结果表明，该框架能够捕获时空动力学，并在单步预测和多步预测场景中均能做出准确预测。