Characterization of Subsurface Hydrogeological Structures With Convolutional Conditional Neural Processes on Limited Training Data

One of the main issues in the application of statistical‐learning‐based methods to the characterization of hydrological phenomena is the complex parameterization of the high‐quality reconstruction. The difficulty of obtaining enough training data and generating multiple‐scale structures hinder the applications of deep‐learning‐based methods in hydrogeological modeling. Hydrogeological modeling problems can be regarded as stochastic processes, and we propose a novel hydrogeological modeling approach based on convolutional conditional neural processes (GM‐ConvCNPs), a meta‐learning approach for dealing with stochastic processes. In this work, GM‐ConvCNP is used to reconstruct the entire spatial structures of subsurface hydrological attributes and channels from a limited amount of conditioning data. To achieve 3‐D characterization of subsurface structures, 3‐D GM‐ConvCNP is proposed according to the spatial distribution characteristics of 3‐D conditioning data. Compared to other deep‐learning‐based methods, we use a small amount of training data and obtain positive model generalization capabilities. Four data sets of categorical and continuous hydrogeological structures are exploited in the experiments. Various validation tests including variograms, connectivity functions, and multi‐dimensional scaling (MDS) map are used to evaluate the quality of generated realizations. The proposed approach is able to significantly reduce training consumption and improve the performance of realizations compared to a set of different benchmark tests. The experiments confirm that the GM‐ConvCNP model can extract heterogeneous patterns by using meta‐learning from limited training data and reconstruct multiple‐scale hydrogeological structures. A case study demonstrates that our method can be applied to characterize multiple‐source hydrological variables.