Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Data
This work addresses the problem of unreliable spatiotemporal forecasting in high-dimensional data for researchers and practitioners, offering a theoretically grounded approach that is incremental in combining domain knowledge with existing deep learning methods.
The paper tackles the lack of theoretical guarantees in deep learning for spatiotemporal predictive learning by designing a Spatiotemporal Observer framework that integrates dynamical system theory, providing generalization error bounds and convergence guarantees, with experimental results showing accurate predictions in one-step-ahead and multi-step-ahead forecasting scenarios.
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.