Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Data

TL;DR

This paper introduces a theoretically grounded deep learning framework called Spatiotemporal Observer for high-dimensional data prediction, integrating dynamical system knowledge to ensure guarantees and improve learning of system dynamics.

Contribution

It proposes a novel observer theory-guided deep learning architecture with error bounds, convergence guarantees, and dynamical regularization for spatiotemporal forecasting.

Findings

Provides generalization error bounds and convergence guarantees.

Effectively captures spatiotemporal dynamics for accurate predictions.

Improves learning of system dynamics through dynamical regularization.

Abstract

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.