Deep transfer learning for groundwater flow in heterogeneous aquifers using a simple analytical model

Abstract

Deep learning models exhibit good interpolating ability, but their performance is often hindered by the scarcity of data in groundwater problems. Analytical models (solutions) provide a first-order physical principle for groundwater flow, but they are only applicable under specific conditions, such as when the aquifer is homogeneous. This study introduces a novel framework for deep transfer learning that integrates the strengths of both methods and overcomes their limitations. Specifically, we propose a deep learning model guided by a simple analytical model to predict groundwater flow in heterogeneous aquifers. It differs from previous deep learning model by incorporating the knowledge from the simple analytical model and utilizing transfer learning technique to improve the prediction in relatively complicated problems where the analytical model is not applicable. The model is tested against the traditional deep learning model Deep Back Propagation Neural Network (DBPNN) in the scenarios with unknown hydraulic conductivity fields. The results show that the proposed model significantly improve the accuracy of hydraulic head predictions by fusing analytical knowledge with neural networks. The hydraulic conductivity mainly affects the parameters of the shallow layers in the neural network, which enables the use of transfer learning techniques in more complex problems. In all test scenarios, the prediction errors of the proposed model are much smaller than those of the DBPNN. Additionally, the proposed model performs satisfactorily even with limited training data.