Review: Theory-guided machine learning applied to hydrogeology-state of the art, opportunities and future challenges

Thanks to recent technological advances, hydrogeologists now have access to large amounts of data acquired in real time. Processing these data using traditional modelling tools is difficult and poses a number of challenges especially for tasks such as extracting useful features, uncertainty quantification or identifying links between variables. Artificial intelligence, and more specifically its subset 'machine learning (ML)', may represent a way of the future in hydrogeological research and applications. Unfortunately, several aspects of machine-learning methods hamper its adoption as a complementary tool for hydrogeologists, namely the black-box nature of most models, an often-limited generalization ability, a hypothetical convergence, and uncertain transferability. Recently, an entirely novel paradigm in the field of machine learning has been identified-theory-guided machine learning-in which the models integrate some specific theoretical knowledge, laws or principles of the field of study. This review article sets out to examine three theory-guided methods in their ability to overcome the limitations of machine learning for hydrogeological research and applications. These methods are, respectively, theory-guided constrained optimization (TGCO), theory-guided refinement of outputs (TGRO) and theory-guided architecture (TGA). The analyses led to the following conclusions: the opacity of ML models can be reduced by any of the three theory-guided ML methods; convergence and generalizability can be enhanced by TGCO, TGA, or a combination of at least two of the theory-guided ML methods; and no study conducted to date has made it possible to deduce the effectiveness of these methods on the transferability of ML models.