Bayesian ensemble machine learning-assisted deterministic and stochastic groundwater DNAPL source inversion with a homotopy-based progressive search mechanism

Abstract

A hyperheuristic homotopy algorithm (HH-HA) and a homotopy-based swarm intelligence algorithm for parallel stochastic search are proposed to improve the search ergodicity and stability of deterministic and stochastic inversion approaches, respectively, for the identification of dense nonaqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Meanwhile, a Bayesian ensemble machine learning (BEML) method for numerical simulation surrogate modeling is proposed to enhance the learning and generalization capability, while significantly reducing the computational cost of repetitive CPU-demanding likelihood evaluations in inversion iterations. Two cases are presented for the verification and application of the proposed inverse modeling methods. The results show that the BEML surrogate model is powerful in approximating the numerical model outputs, reducing the mean relative errors of the contaminant concentration and pressure head predictions to 1.18% and 1.29%, respectively. The homotopy-based progressive search mechanism is highly effective in achieving more accurate identification values for deterministic inversion and a more reliable posterior distribution for stochastic inversion. The HH-HA shows stable performance, approaching the global optimum in wide areas and reducing the mean relative error of identification from 11.95% to 4.11%. The homotopy-based parallel stochastic search lines adequately cover the search space tracking the change of homotopy parameter, and the mean relative error of point estimation is reduced to 2.03%. Though the deterministic inversion approach can provide intuitive identification values, the reliability of the inversion outputs cannot be quantified. In contrast, the proposed stochastic inversion system is of great significance for providing decision makers with comprehensive reference information.