用卷积网络从稀疏观测点预测完整空间场，无需先验知识。
Visual Spatial Learning: Single-Field Spatial Interpolation Using Convolutional Neural Networks
- 基于CNN直接学习单个空间场的插值，无需外部数据。
- 在非平稳场景下表现优于传统克里金法，不依赖协方差建模。
- 适合缺乏领域知识、需快速部署的空间预测任务。
从稀疏观测中预测完整的空间相关场是空间统计与环境建模中的基础挑战。经典插值方法如克里金法依赖高斯过程假设和变差分析，难以应对非平稳情形，且需大量领域知识。本文提出一种基于卷积神经网络（CNN）的空间插值架构，仅需一个部分观测的空间场即可训练与应用，无需外部数据或历史场。模型在观测点上直接监督，学习预测用户定义网格上的未观测点值。相比克里金法，该方法无需显式协方差建模或变差函数估计，能灵活捕捉局部空间模式。实验表明，该方法在稀疏监督下实现单实例空间插值，为传统地理统计方法提供实用替代方案，并将CNN扩展至新问题领域。
原文摘要 · Abstract (English)
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.
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