Efficient Large-scale Nonstationary Spatial Covariance Function
  Estimation Using Convolutional Neural Networks
Pratik Nag Yiping Hong Sameh Abdulah Ghulam A. Qadir Marc G. Genton Ying Sun
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.