Modelling clogging dynamics in groundwater systems using multiscale homogenized physics informed neural network (MHPINN)

Abstract

Groundwater systems, or also commonly known as large-scale closed and saturated porous media systems in general, are important sources of potable water, especially in arid countries. However, maintenance of groundwater systems is operationally expensive and time-consuming, hence requiring field engineers to optimally predict the system's breakthrough phase. To address this engineering challenge, this study developed an alternative physics informed machine learning model, termed as multiscale homogenized physics informed neural network (MHPINN), to model and predict the effluent discharge concentrations from closed and saturated porous media systems when removing different contaminants. The proposed MHPINN model mainly exploits the homogenization theory, coupled with multiscale perturbation analysis, for hydrodynamic modelling to extract important model input features pertaining to the pore-scale clogging behavior in porous media. Together with available experimental data, the extracted model features then set the input layer for training neural network model to predict the discharge concentration of emulated porous media groundwater systems. At the same time, the model training is performed with modified mean square error (MSE) cost function, based upon homogenized mathematical representations derived from a series of rigorous mathematical constructs and formulations, to better facilitate the model's learning, especially under sparse data constraint. To verify the proposed methodology, MPINN is trained (and validated) with data obtained from five historical experimental studies, which emulated porous media systems to remove ammonium ions and fine-scaled colloids, to model and predict the discharge concentration in each study. Overall, MHPINN outperformed other conventional machine learning models (random forest, support vector machines, etc.) by obtaining higher predictive accuracy of around 4% on average from the model's validation step across the five different experimental studies. Therefore, the predictive analysis underscored the effectiveness of MHPINN to combine both physics-based modelling and machine learning to model complex porous media systems, under sparse experimental data constraints, hence demonstrating the potential of the proposed methodology to extend to other physical systems.