  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.
