Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Data

Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the frameworks of those models are mainly designed 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 demonstrate that this framework could effectively model the spatiotemporal dynamics and make accurate predictions in both one-step-ahead and multi-step-ahead forecasting scenarios. © 2025 IEEE.