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.

翻译：在气候与环境科学等众多领域观测到的空间过程通常呈现大规模特征，且表现出空间非平稳性。采用非平稳Matérn协方差的高斯过程拟合极具挑战性。现有文献通过空间分割技术来估计协方差函数中空间变化的参数。分区选择虽至关重要，却往往依赖主观判断，缺乏数据驱动方法。针对这一问题，本研究利用卷积神经网络（ConvNets）从非平稳数据中推导子区域。我们采用选择机制识别与平稳场具有相似表现的子区域。为区分平稳与非平稳随机场，我们使用多种模拟数据对ConvNet进行训练。这些模拟数据来自不同参数设置下的Matérn协方差模型高斯过程，确保充分覆盖平稳与非平稳空间数据的代表性特征。我们通过大规模合成数据集与真实数据集评估所提方法性能。结果表明，相较传统人为定义的分区方式，基于ConvNet的分区方法在参数估计中展现出更高精度。