Theory-guided full convolutional neural network: An efficient surrogate model for inverse problems in subsurface contaminant transport

Identification of the location and strength of a contaminant source in an aquifer is a challenging but crucial task. Efficient surrogate models can be constructed to replace traditional time-consuming simulators while solving this inverse problem. In recent years, with the rapid development of machine learning (ML) algorithms, the artificial neural network (ANN) has been proven to be an efficient way for surrogate modeling. However, it may be difficult for ANN-based algorithms to learn the convection-dispersion equation and predict the contaminant concentration field due to their point-to-point learning scheme. Because of their strong localized features, the concentration fields can be seen as images. In contrast, the convolutional neural network (CNN) can extract spatial information better due to its convolutional structure. Herein, a theory-guided full convolutional neural network (TgFCNN) model is proposed to solve inverse problems in subsurface contaminant transport. TgFCNN can construct robust and reliable surrogate models with limited training realizations, and be further utilized for inverse modeling tasks. The loss function of TgFCNN comprises the residual of governing equations of contaminant transport, as well as data mismatch. Moreover, the iterative ensemble smoother (IES) method is employed to update the parameters while solving the inverse problems. The proposed TgFCNN model is evaluated in four scenarios. The results demonstrate that the TgFCNN model possesses strong generalization and extrapolation abilities, and satisfactory accuracy when estimating unknown contaminant source parameters, as well as the permeability field. The time consumption of the TgFCNN surrogate model for inverse tasks is also greatly reduced compared to using traditional simulators directly.