Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

TL;DR

This paper introduces a Bayesian RNN framework for forecasting complex spatio-temporal systems and provides a rigorous approach to quantify uncertainty while maintaining high forecast accuracy.

Contribution

It develops a Bayesian RNN model tailored for nonlinear spatio-temporal data, addressing the gap in uncertainty quantification in existing RNN applications.

Findings

Successful application to Lorenz simulation data

Effective uncertainty quantification in real-world datasets

Maintains forecast accuracy with Bayesian approach

Abstract

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications.