# Efficient Large-scale Nonstationary Spatial Covariance Function Estimation Using Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2306.11487 · HTML: https://mlsanity.com/paper/2306.11487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Joint Face Detection and Alignment using Multi-task Cascaded Convolutional Networks](https://mlsanity.com/paper/1604.02878/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [Pixie: A System for Recommending 3+ Billion Items to 200+ Million Users in Real-Time](https://mlsanity.com/paper/1711.07601/) (2017)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches](https://mlsanity.com/paper/1610.02447/) (2016)
- [Towards black-box parameter estimation](https://mlsanity.com/paper/2303.15041/) (2023)
- [ExaGeoStat: A High Performance Unified Software for Geostatistics on Manycore Systems](https://mlsanity.com/paper/1708.02835/) (2017)
- [Hierarchical low rank approximation of likelihoods for large spatial datasets](https://mlsanity.com/paper/1605.08898/) (2016)
- [Large-scale Environmental Data Science with ExaGeoStatR](https://mlsanity.com/paper/1908.06936/) (2019)
- [Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment](https://mlsanity.com/paper/1911.02249/) (2019)
- [Scalable Deep Gaussian Markov Random Fields for General Graphs](https://mlsanity.com/paper/2206.05032/) (2022)
- [A Generalized Convolution Model and Estimation for Non-stationary Random Functions](https://mlsanity.com/paper/1412.1373/) (2014)
- [Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components](https://mlsanity.com/paper/2210.08231/) (2022)

## Built on by (most cited first, 1 of 1)

- [Modeling nonstationary spatial processes with normalizing flows](https://mlsanity.com/paper/2509.12884/) (2025)

## Abstract (arXiv)

Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat'ern covariance is challenging. Previous studies in the literature have tackled this challenge by employing spatial partitioning techniques to estimate the parameters that vary spatially in the covariance function. The selection of partitions is an important consideration, but it is often subjective and lacks a data-driven approach. To address this issue, in this study, we utilize the power of Convolutional Neural Networks (ConvNets) to derive subregions from the nonstationary data. We employ a selection mechanism to identify subregions that exhibit similar behavior to stationary fields. In order to distinguish between stationary and nonstationary random fields, we conducted training on ConvNet using various simulated data. These simulations are generated from Gaussian processes with Mat'ern covariance models under a wide range of parameter settings, ensuring adequate representation of both stationary and nonstationary spatial data. We assess the performance of the proposed method with synthetic and real datasets at a large scale. The results revealed enhanced accuracy in parameter estimations when relying on ConvNet-based partition compared to traditional user-defined approaches.