Surrogate models, physics-informed neural networks and climate change

This research contributes to the advancement of surrogate modelling as a powerful technique in the field of computational simulation that offers numerous advantages for solving complex problems efficiently. In particular, this study emphasizes the pivotal role of surrogate modeling in groundwater management. By integrating key factors like climate change and leveraging machine learning, particularly neu-ral networks, the research facilitates more informed decision-making, significantly reducing the computational cost of complex numerical models. The impact of climate change is a central focus and the first study aims to construct surrogate data-driven models for evaluating climate change effects on groundwater resources, also in the future. The study involves a comparison between statistical methods and different types of artificial neural networks (ANNs). The ef-fectiveness of surrogate models was demonstrated in Northern Tuscany (Italy) but can easily extend to any area of interest. The adopted statistical method involves analyzing historical precipitation and temperature data along with groundwater levels recorded in monitoring wells. Initially, the study explores potential correla-tions between meteorological and groundwater indices; if a correlation is identified, a linear regression analysis is employed to establish relationships between them. These established relationships are then used to estimate future groundwater le-vels based on projected precipitation and temperature obtained from an ensemble of Regional Climate Models, under two Representative Concentration Pathways, namely RCP4.5 and RCP8.5. Then, three distinct Artificial Intelligence (AI) models, Nonlinear AutoRegres-sive with eXogenous inputs (NARX), Long-Short Term Memory (LSTM) and Con-volutional Neural Network (CNN) were implemented to evaluate the impact of cli-mate change on groundwater resources for the same case study. Specifically, these models were trained using directly historical precipitation and temperature data as input to provide groundwater levels as output. Following the training phase, the developed AI models were utilized to forecast future groundwater levels using the same precipitation and temperature projections and climate scenarios described above. The results highlighted different outputs among the models used in this work. However, most of them predict a decrease in groundwater levels as a result of future variations in precipitation and temperature. The study also presents the strengths and weaknesses of each model. Notably, the LSTM model emerges as the most promising approach to predict future groundwater levels. Within the same field, an ANN was developed with the capability to simulate groundwater conditions in the Konya closed basin, Turkey, one of the pilot sites investigated as part of the InTheMED project. This model serves as a tool for examining the potential impacts of climate change and agricultural policies on groundwater resources within the region. The final goal of this application, is to provide a user-friendly tool, based on the trained neural network. The inherent simplicity of the surrogate model, with a straightforward interface and results that are simple to understand, plays a crucial role in decision-making processes. Shifting to pollutant transport, an ANN was implemented to solve different direct and inverse problems. The direct problem deals with the evaluation of con-centrations in monitoring wells, while the inverse problem involves the identifica-tion of contaminant sources and their release history. It demonstrated efficiency in addressing both direct and inverse transport problems, offering reliable results with reduced computational burden. The study also addresses the interpretability challenge of ANNs and the so ca-lled “generalization problem” through Physics-Informed Neural Networks (PINNs). By incorporating physics-based constraints, PINNs bridge the gap between data-driven modeling and physics-based interpretations, offering a promising approach for groundwater numerical simulations. In this study, a PINN is developed to si-mulate flow in an unconfined aquifer. Finally, two extra content are presented. First, an ANN is used to solve an inverse problem in the field of sewer systems. Then, an easily interpretable exam-ple of numerical groundwater flow modeling using spreadsheets, from a didactic perspective, is described. In conclusion, this research underscores the importance of surrogate modeling, machine learning, climate change analysis, and physics-informed approaches in ad-vancing groundwater management strategies and beyond, providing valuable tools for decision-makers to address complex groundwater flow problems in changing environmental conditions.