Comparing numerical modelling, traditional machine learning and theory-guided machine learning in inverse modeling of groundwater dynamics: A first study case application

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This study proposes to test the hypothesis that theory-guided machine learning model can be effectively applied to model the behavior of a real aquifer. For this purpose, a theory-guided multilayer perceptron model (TgMLP) for real aquifers was developed to simulate groundwater flow dynamics. A comparison of the performance of the TgMLP with that of a numerical model (NumMod) and a traditional multilayer perceptron model (MLP) was performed. The ability of these three models to capture the spatiotemporal dynamics of groundwater was evaluated, the degree of PDE violation of the TgMLP model was also assessed, and the applicability of these three models in a real-world setting was discussed. The Saint-Honoré unconfined aquifer (Quebec, Canada), which has been extensively monitored over the last few years, was used as an experimental laboratory for this study. Historical groundwater levels, recharge, precipitation, mean temperature and streamflow data were used to calibrate/train/validate and test the models. The results show that the performance of the TgMLP far exceeds that of the numerical and traditional MLP models, that the MLP model is a good interpolator but is unable to extrapolate, and that only the numerical and TgMLP models are able to capture the spatiotemporal dynamics of groundwater flow and represent the dominant flow direction in the aquifer. It was found that the TgMLP model better approximates the solution of the PDE at 70% of the locations. These results support the hypothesis that TgMLP is effective in modeling the spatiotemporal dynamics of groundwater in a real aquifer even if improvements are needed. Although the TgMLP model is capable of representing groundwater flow dynamics to some degree, its implementation requires much higher computational costs than a numerical model; however, these can be reduced with the use of a GPU to speed up the calculations.