# Scalable Spatiotemporal Prediction with Bayesian Neural Fields

arXiv: https://arxiv.org/abs/2403.07657 · HTML: https://mlsanity.com/paper/2403.07657/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions](https://mlsanity.com/paper/1905.06076/) (2019)
- [Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data](https://mlsanity.com/paper/1711.00636/) (2017)
- [Bayesian Computing with INLA: A Review](https://mlsanity.com/paper/1604.00860/) (2016)
- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [ProbNeRF: Uncertainty-Aware Inference of 3D Shapes from 2D Images](https://mlsanity.com/paper/2210.17415/) (2022)
- [An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications](https://mlsanity.com/paper/2209.12565/) (2022)
- [Constructing Large Nonstationary Spatio-Temporal Covariance Models via Compositional Warpings](https://mlsanity.com/paper/2202.03560/) (2022)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)

## Built on by (most cited first, 10 of 10)

- [Learning dynamical systems with hit-and-run random feature maps](https://mlsanity.com/paper/2501.06661/) (2025)
- [A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting](https://mlsanity.com/paper/2506.00798/) (2025)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [Simple and Robust Forecasting of Spatiotemporally Correlated Small Earth Data with A Tabular Foundation Model](https://mlsanity.com/paper/2510.08920/) (2025)
- [Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training](https://mlsanity.com/paper/2512.05132/) (2025)
- [Towards High Resolution Probabilistic Coastal Inundation Forecasting from Sparse Observations](https://mlsanity.com/paper/2505.05381/) (2025)
- [Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty](https://mlsanity.com/paper/2506.11761/) (2025)
- [Spatio-temporal, multi-field deep learning of shock propagation in meso-structured media](https://mlsanity.com/paper/2509.16139/) (2025)
- [Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification](https://mlsanity.com/paper/2511.02175/) (2025)
- [Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance](https://mlsanity.com/paper/2607.25376/) (2026)

## Abstract (arXiv)

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in diverse applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As the scale of modern datasets increases, there is a growing need for statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle many observations. This article introduces the Bayesian Neural Field (BayesNF), a domain-general statistical model that infers rich spatiotemporal probability distributions for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust predictive uncertainty quantification. Evaluations against prominent baselines show that BayesNF delivers improvements on prediction problems from climate and public health data containing tens to hundreds of thousands of measurements. Accompanying the paper is an open-source software package (https://github.com/google/bayesnf) that runs on GPU and TPU accelerators through the JAX machine learning platform.