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Flood mapping on Earth imagery is crucial for disaster management, but its efficacy is hampered by the lack of high-quality training labels. Given high-resolution Earth imagery with coarse and noisy training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the true high-resolution labels while training neural network parameters. Traditional methods are largely based on specific physical properties and thus fall short of capturing the rich domain constraints expressed by symbolic logic. Neural-symbolic models can capture rich domain knowledge, but existing methods do not address the unique spatial challenges inherent in flood mapping on high-resolution imagery. To fill this gap, we propose a spatial-logic-aware weakly supervised learning framework. Our framework integrates symbolic spatial logic inference into probabilistic learning in a weakly supervised setting. To reduce the time costs of logic inference on vast high-resolution pixels, we propose a multi-resolution spatial reasoning algorithm to infer true labels while training neural network parameters. Evaluations of real-world flood datasets show that our model outperforms several baselines in prediction accuracy. The code is available at https://github.com/spatialdatasciencegroup/SLWSL. 

Spatial classification with limited observations is important in geographical applications where only a subset of sensors are deployed at certain spots or partial responses are collected in field surveys. For example, in observation-based flood inundation mapping, there is a need to map the full flood extent on geographic terrains based on earth imagery that partially covers a region. Existing research mostly focuses on addressing incomplete or missing data through data cleaning and imputation or modeling missing values as hidden variables in the EM algorithm. These methods, however, assume that missing feature observations are rare and thus are ineffective in problems whereby the vast majority of feature observations are missing. To address this issue, we recently proposed a new approach that incorporates physics-aware structural constraint into the model representation. We design efficient learning and inference algorithms. This paper extends our recent approach by allowing feature values of samples in each class to follow a multi-modal distribution. Evaluations on real-world flood mapping applications show that our approach significantly outperforms baseline methods in classification accuracy, and the multi-modal extension is more robust than our early single-modal version. Computational experiments show that the proposed solution is computationally efficient on large datasets. 

Accurate maps of regional surface water features are integral for advancing ecologic, atmospheric and land development studies. The only comprehensive surface water feature map of Alaska is the National Hydrography Dataset (NHD). NHD features are often digitized representations of historic topographic map blue lines and may be outdated. Here we test deep learning methods to automatically extract surface water features from airborne interferometric synthetic aperture radar (IfSAR) data to update and validate Alaska hydrographic databases. U-net artificial neural networks (ANN) and high-performance computing (HPC) are used for supervised hydrographic feature extraction within a study area comprised of 50 contiguous watersheds in Alaska. Surface water features derived from elevation through automated flow-routing and manual editing are used as training data. Model extensibility is tested with a series of 16 U-net models trained with increasing percentages of the study area, from about 3 to 35 percent. Hydrography is predicted by each of the models for all watersheds not used in training. Input raster layers are derived from digital terrain models, digital surface models, and intensity images from the IfSAR data. Results indicate about 15 percent of the study area is required to optimally train the ANN to extract hydrography when F1-scores for tested watersheds average between 66 and 68. Little benefit is gained by training beyond 15 percent of the study area. Fully connected hydrographic networks are generated for the U-net predictions using a novel approach that constrains a D-8 flow-routing approach to follow U-net predictions. This work demonstrates the ability of deep learning to derive surface water feature maps from complex terrain over a broad area.