Deep learning for Earth imagery plays an increasingly important role in geoscience applications such as agriculture, ecology, and natural disaster management. Still, progress is often hindered by the limited training labels. Given Earth imagery with limited training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the full labels while training the neural network. The problem is challenging due to the sparse and noisy input labels, spatial uncertainty within the label inference process, and high computational costs associated with a large number of sample locations. Existing works on neuro-symbolic models focus on integrating symbolic logic into neural networks (e.g., loss function, model architecture, and training label augmentation), but these methods do not fully address the challenges of spatial data (e.g., spatial uncertainty, the trade-off between spatial granularity and computational costs). To bridge this gap, we propose a novel Spatial Knowledge-Infused Hierarchical Learning (SKI-HL) framework that iteratively infers sample labels within a multi-resolution hierarchy. Our framework consists of a module to selectively infer labels in different resolutions based on spatial uncertainty and a module to train neural network parameters with uncertainty-aware multi-instance learning. Extensive experiments on real-world flood mapping datasets show that the proposed model outperforms several baseline methods. The code is available at \url{https://github.com/ZelinXu2000/SKI-HL}.

提出了一种新颖的基于空间知识的分层学习（SKI-HL）框架，该框架采用多分辨率层次结构迭代地推断样本标签，并在具有不确定性感知的多实例学习中训练神经网络参数。实验证明，该模型在真实世界的洪水图像数据集上优于几种基准方法。

融合空间知识的层次学习：地球影像中的洪水测绘应用