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

arXiv: https://arxiv.org/abs/1711.00636 · HTML: https://mlsanity.com/paper/1711.00636/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2017.

## Built on by (most cited first, 17 of 17)

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- [Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations](https://mlsanity.com/paper/2412.07265/) (2024)
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- [Neural Ordinary Differential Equations for Modeling Socio-Economic Dynamics](https://mlsanity.com/paper/2604.00632/) (2026)

## Abstract (arXiv)

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.