An ensemble optimizer with a stacking ensemble surrogate model for identification of groundwater contamination source

The application of the simulation-optimization method for groundwater contamination source identification (GCSI) encounters two main challenges: the substantial time cost of calling the simulation model, and the limitations on the accuracy of identification results due to the complexity, nonlinearity, and ill-posed nature of the inverse problem. To address these issues, we have innovatively developed an inversion framework based on ensemble learning strategies. This framework comprises a stacking ensemble model (SEM), which integrates three distinct machine learning models (Extremely Randomized Trees, Adaptive Boosting, and Bidirectional Gated Recurrent Unit), and an ensemble optimizer (E-GKSEEFO), which combines two newly proposed swarm intelligence optimizers (Genghis Khan Shark Optimizer and Electric Eel Foraging Optimizer). Specifically, the SEM serves as a surrogate model for the groundwater numerical simulation model. Compared to the original simulation model, it significantly reduces time cost while maintaining accuracy. The E-GKSEEFO, functioning as the search strategy for the optimization model, greatly enhances the accuracy of the optimization results. We have verified the performance of the SEM-E-GKSEEFO ensemble inversion framework through two hypothetical scenarios derived from an actual coal gangue pile. The results are as follows. (1) The SEM exhibits improved fitting performance compared to single machine learning models when dealing with high-dimensional nonlinear data from GCSI. (2) The E-GKSEEFO achieves significantly higher accuracy in the identification results of GCSI than individual optimizers. These findings affirm the effectiveness and superiority of the proposed SEM-EGKSEEFO ensemble inversion framework.