Groundwater contamination source identification based on Sobol sequences-based sparrow search algorithm with a BiLSTM surrogate model

In the traditional linked simulation-optimization method, solving the optimization model requires massive invoking of the groundwater numerical simulation model, which causes a huge computational load. In the present study, a surrogate model of the origin simulation model was developed using a bidirectional long and short-term memory neural network method (BiLSTM). Compared with the surrogate models built by shallow learning methods (BP neural network) and traditional LSTM methods, the surrogate model built by BiLSTM has higher accuracy and better generalization performance while reducing the computational load. The BiLSTM surrogate model had the highest R-2 of the three with 0.9910 and the lowest RMSE with 3.7732 g/d. The BiLSTM surrogate model was linked to the optimization model and solved using the sparrow search algorithm based on Sobol sequences (SSAS). SSAS enhances the diversity of the initial population of sparrows by introducing Sobol sequences and introduces nonlinear inertia weights to control the search range and search efficiency. Compared with SSA, SSAS has stronger global search ability and faster search efficiency. And SSAS identifies the contamination source location and release intensity stably and reliably. The average relative error of SSAS for the identification of source location is 9.4%, and the average relative error for the identification of source intensity is 1.83%, which are both lower than that of SSA at 11.12% and 3.03%. This study also applied the Cholesky decomposition method to establish a Gaussian field for hydraulic conductivity to evaluate the feasibility of the simulation-optimization method.