A deep adaptive bidirectional generative adversarial neural network (Bi-GAN) for groundwater contamination source estimation

Groundwater contaminant source estimation (GCSE) plays a vital role in the risk assessment and remediation of groundwater contamination. GCSE involves determining the optimal values of unknown variables that result in the observed contaminant concentrations at monitoring wells. This can be achieved by establishing an inverse mapping from the observed concentrations to the unknown variables characterizing the contaminant source. In recent years, deep learning such as generative adversarial neural network (GAN) has gained increasing attention as an effective tool for establishing inverse mapping relationships between observed contaminant distributions and source-related parameters. While a single-directional GAN can effectively establish this inverse mapping relationship, it faces a significant limitation in that the inverse results cannot be validated by comparing the corresponding simulation outputs with the observed contaminant concentrations, which is crucial for ensuring accuracy and reliability in real-world GCSE applications. To address this issue, we propose a bidirectional generative adversarial neural network (Bi-GAN) that incorporates both an inversion process and a forward process, enhancing the supervision of the inverse mapping. Specifically, the inversion process produces unknown variables estimates (generated data) from the observed contaminant concentrations, while the forward process converts these estimates into the corresponding simulation outputs. The forward process then evaluates the similarity between the simulation outputs and observed concentrations. This similarity measure informs the training of the inversion process, ensuring greater accuracy. Once the model meets the accuracy threshold, the inversion process can be extracted for providing reliable GCSE estimations. In addition, the performance of Bi-GAN is strongly influenced by the quality of its training samples. To optimize this, we introduced an adaptive sampling strategy, which significantly improves the quality of the training data, resulting in enhanced accuracy for GCSE (50 % error reduction in case 1 and 70 % error reduction in case 2). Furthermore, the data-driven nature of the Bi-GAN allows for a substantial reduction in inversion inference time cost during the estimation process. The proposed Bi-GAN framework was evaluated using two hypothetical cases: a heterogeneity with zone partitioning case (case 1) and a heterogeneity with continuous medium case (case 2), aiming to provide an efficient, accurate, and cost-effective solution for GCSE. The results demonstrate that Bi-GAN delivers superior performance, achieving high estimation accuracy (0.87 % ARE in case 1 and 3.62 % ARE in case 2) and remarkable computational efficiency (0.05 s and 0.07 s inversion inference time). These results are particularly noteworthy when compared with traditional inversion methods in GCSE such as the ensemble kalman filter (EnKF) and the genetic algorithm (GA).