Neural Networks for Parameter Estimation in Geometrically Anisotropic Geostatistical Models

TL;DR

This paper introduces a neural network method for estimating covariance functions in anisotropic geostatistical models, extending previous isotropic approaches to handle directionally varying correlation structures, validated through simulations and real data.

Contribution

It presents a novel neural network approach for anisotropic covariance estimation in spatial Gaussian fields, broadening the scope beyond isotropic models.

Findings

Effective estimation of anisotropic covariance functions demonstrated.

Method performs well on both simulated and real datasets.

Provides practical guidelines for geostatistical analysis.

Abstract

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely isotropic setting to encompass geometrically anisotropic correlation structures, i.e., random fields with correlation ranges that vary across different directions. We conduct experiments with both simulated and real data to assess the performance of the methodology and to provide guidelines to practitioners.