Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and variography, which can limit their effectiveness in non-stationary settings and require substantial domain expertise. In this work, we leverage an architecture based on convolutional neural networks (CNNs) for spatial interpolation that is trained and applied on a single partially observed field, without access to external data or prior fields. The model is supervised directly on the observed locations and learns to predict values at unobserved points on the user defined grid. Unlike Kriging, our method does not require explicit covariance modelling or variogram estimation, and it can flexibly capture local spatial patterns in a data-driven manner. This work demonstrates the potential of CNNs for single-instance spatial interpolation under sparse supervision, offering a practical alternative to classical geostatistical methods, and extending the use of CNNs to a new problem domain.

翻译：根据稀疏观测数据预测完整空间相关场是空间统计与环境建模中的基本挑战。克里金等经典插值方法依赖于高斯过程假设与变异函数分析，这可能导致其在非平稳场景下效果受限，且需要大量领域专业知识。本研究利用基于卷积神经网络（CNN）的架构进行空间插值，该模型在单一部分观测场域上进行训练与应用，无需依赖外部数据或先验场域信息。模型直接以观测位置作为监督信号，自主习得在用户定义网格上预测未观测点数值的能力。与传统克里金方法不同，本方法无需显式协方差建模或变异函数估计，能以数据驱动方式灵活捕捉局部空间模式。本研究论证了CNN在稀疏监督条件下实现单实例空间插值的潜力，为经典地统计方法提供了实用替代方案，并将CNN的应用拓展至全新的问题领域。