Neural networks for geospatial data | JoVE Visualize

Area of Science:

Geostatistics
Machine Learning
Spatial Data Analysis

Background:

Traditional geospatial analysis relies on model-based approaches with linear mean functions and Gaussian Process (GP) covariance.
Current nonlinear machine learning methods often omit explicit spatial covariance modeling, limiting their applicability in geostatistics.
There is a need for methods that integrate nonlinear machine learning with established GP frameworks for spatial data.

Purpose of the Study:

To propose Neural Network Generalized Least Squares (NN-GLS), a novel framework embedding neural networks within GP models.
To enable the accommodation of nonlinear mean functions in geostatistical analysis while preserving GP advantages like spatial covariance modeling and kriging.
To provide a theoretically grounded and computationally efficient approach for analyzing irregular geospatial data.

Main Methods:

NN-GLS embeds neural networks into the GP framework, using a Generalized Least Squares (GLS) loss to account for spatial covariance in parameter estimation.
The method establishes a connection between NN-GLS and Graph Neural Networks (GNNs), enabling scalable computation for irregular spatial data.
Methodology for uncertainty quantification in estimation and prediction is developed, alongside theoretical consistency and finite sample concentration rate proofs.

Main Results:

NN-GLS successfully integrates nonlinear mean functions into GP models, retaining explicit spatial covariance modeling and kriging capabilities.
The GNN representation facilitates efficient, scalable computation for irregular spatial data using standard neural network techniques.
Theoretical results confirm the consistency of NN-GLS for irregularly observed, spatially correlated data, with quantified finite sample properties.

Conclusions:

NN-GLS offers a powerful, unified approach for nonlinear geostatistical modeling, outperforming existing methods in handling complex spatial dependencies.
The framework provides robust uncertainty quantification and is computationally scalable, demonstrated through simulations and air pollution modeling.
The development of the Python package geospaNN makes NN-GLS accessible for practical geospatial analysis applications.