# Neural networks for geospatial data

arXiv: https://arxiv.org/abs/2304.09157 · HTML: https://mlsanity.com/paper/2304.09157/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [A GNN-RNN Approach for Harnessing Geospatial and Temporal Information: Application to Crop Yield Prediction](https://mlsanity.com/paper/2111.08900/) (2021)
- [Gaussian Process Boosting](https://mlsanity.com/paper/2004.02653/) (2020)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Graphical Gaussian Process Models for Highly Multivariate Spatial Data](https://mlsanity.com/paper/2009.04837/) (2020)
- [Forecasting West Nile Virus with Graph Neural Networks: Harnessing Spatial Dependence in Irregularly Sampled Geospatial Data](https://mlsanity.com/paper/2212.11367/) (2022)
- [Spatial disease mapping using Directed Acyclic Graph Auto-Regressive (DAGAR) models](https://mlsanity.com/paper/1704.07848/) (2017)
- [Random forests for binary geospatial data](https://mlsanity.com/paper/2302.13828/) (2023)

## Built on by (most cited first, 11 of 11)

- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Multivariate Probabilistic Time Series Forecasting with Correlated Errors](https://mlsanity.com/paper/2402.01000/) (2024)
- [Better Batch for Deep Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2305.17028/) (2023)
- [Kriging prior Regression: A Case for Kriging-Based Spatial Features with TabPFN in Soil Mapping](https://mlsanity.com/paper/2509.09408/) (2025)
- [Pedestrian Volume Prediction Using a Diffusion Convolutional Gated Recurrent Unit Model](https://mlsanity.com/paper/2411.03360/) (2024)
- [A Subsampling Based Neural Network for Spatial Data](https://mlsanity.com/paper/2411.03620/) (2024)
- [Can We Predict the Unpredictable? Leveraging DisasterNet-LLM for Multimodal Disaster Classification](https://mlsanity.com/paper/2506.23462/) (2025)
- [Spatiodynamic inference using vision-based generative modelling](https://mlsanity.com/paper/2507.22256/) (2025)
- [TSCoNet: A Two-Stage Copula CNN-LSTM for Uncertainty-Aware Spatio-Temporal Forecasting](https://mlsanity.com/paper/2607.10410/) (2026)
- [Gaussian Process Decorrelation for Spatiotemporal Deep Learning-Based Snow Water Equivalent Prediction](https://mlsanity.com/paper/2609.22182/) (2026)
- [Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2609.36046/) (2026)

## Abstract (arXiv)

Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of linearity and propose embedding neural networks directly within the traditional geostatistical models to accommodate non-linear mean functions while retaining all other advantages including use of Gaussian Processes to explicitly model the spatial covariance, enabling inference on the covariate effect through the mean and on the spatial dependence through the covariance, and offering predictions at new locations via kriging. We propose NN-GLS, a new neural network estimation algorithm for the non-linear mean in GP models that explicitly accounts for the spatial covariance through generalized least squares (GLS), the same loss used in the linear case. We show that NN-GLS admits a representation as a special type of graph neural network (GNN). This connection facilitates use of standard neural network computational techniques for irregular geospatial data, enabling novel and scalable mini-batching, backpropagation, and kriging schemes. Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes. We also provide a finite sample concentration rate, which quantifies the need to accurately model the spatial covariance in neural networks for dependent data. To our knowledge, these are the first large-sample results for any neural network algorithm for irregular spatial data. We demonstrate the methodology through simulated and real datasets.