Identification of time-varying contaminant discharge rates using a data-driven Transformer model

The identification of groundwater contamination sources (IGCS) is a critical prerequisite for the development of contamination remediation strategies and is vital for safeguarding groundwater resources. However, the recurrent neural networks (RNNs) previously applied to address IGCS have limitations due to their requirement for stepwise processing of data and inability to handle parallel processing, which restrict both accuracy and efficiency. This study applies the Transformer model to directly identify groundwater contamination source characteristics. The self-attention mechanism of the Transformer model effectively captures long-range dependencies in input data, overcoming the limitations of step-by-step data processing and supporting parallel processing of sequential information. This advantage allows the Transformer model to capture the dynamic changes in contamination source characteristics (e.g., contaminant discharge rates) across different time steps, resulting in more accurate IGCS. A hypothetical case study is conducted to compare the performance of data-driven methods (Transformer and MLP inverse mapping models) with surrogate-assisted physics-based methods (optimization and data assimilation methods), for identifying contamination source characteristics. The results indicate that the Transformer model performs better in terms of identification accuracy. The data assimilation method provides satisfactory results with a lower computational burden, making it more suitable for scenarios with strict time requirements. The optimization method requires more computational time and produces less accurate identification results compared to the other three methods.