Bayesian hybrid-kernel machine-learning-assisted sensitivity analysis and sensitivity-relevant inverse modeling for groundwater DNAPL contamination

Abstract

Accurate source characterization and transport parameter estimation is important when seeking to predict the spatiotemporal distribution of dense non-aqueous phase liquid (DNAPL) contaminants in groundwater. However, this is a complex multimodal search problem prone to equifinality and premature convergence, which leads to considerable error. To address this, a sensitivity-relevant dynamic swarm intelligence (SRD-SI) algorithm embedded in a homotopy-variation mechanism is proposed in the present study to rationally balance the inversion processes of sensitivity-varied source characteristics and DNAPL transport parameters. In this approach, global optima are progressively approached in conjunction with the homotopy variation of the search space. Furthermore, to avoid computationally expensive numerical model repetition during the sensitivity analysis and inverse iterations, a Bayesian-based optimization framework that combines multiple kernel functions in a kernel extreme learning machine (KELM) model is designed considering the complex site conditions and statistical characteristics of the input variables, thus creating the Bayesian hybrid KELM (BHK-ELM) model for the reliable surrogate modeling of numerical DNAPL-transport simulations. The results show that the BHK-ELM model recognizes and effectively reconstructs the complex input − output mapping of the numerical model by increasing the determination coefficient R2 to 0.9988 while improving the computational efficiency approximately 4500-fold. Because source characteristics and boundary conditions are far more sensitive than transport parameters to the contaminant distribution, conventional inverse modeling methods struggle to accurately identify these transport parameters. In contrast, the proposed inverse modeling system combining sensitivity analysis, swarm intelligence, and homotopy variation is more stable and provides significantly more accurate estimations for all unknown variables. Compared with the traditional SI algorithm, the homotopy-variation SRD-SI reduced the maximum inversion relative error from 46.22 % to 9.53 %, while the mean inversion relative error was reduced from 11.09 % to 3.90 %.