Physics-Informed Neural Networks for solving transient unconfined groundwater flow

Neural networks excel in various machine learning applications; however, they lack the physical interpretability and constraints crucial for numerous scientific and engineering problems. This limitation hinders their ability to accurately capture and predict complex physical systems' behavior, potentially yielding inaccurate or unreliable results. Physics-Informed Neural Networks (PINNs) are a class of machine learning models that integrate the power of neural networks with the physical laws governing natural phenomena. PINNs provide an effective tool for solving intricate physical problems, ranging from fluid dynamics to materials science, by incorporating physical constraints into the neural network architecture. PINNs can substantially enhance the accuracy and efficiency of model predictions, even in data-limited situations. This work offers insight into recent developments in the PINN field, including their mathematical formulation and training algorithms, and emphasizes their application in solving transient unconfined groundwater flow. In this context, the phreatic surface acts as a spatiotemporally varying boundary condition, and properly accounting for its position is vital for precise predictions of unconfined groundwater flow and related environmental and engineering applications. The study's objective is to develop a reliable model for estimating the phreatic surface and the spatiotemporal distribution of piezometric heads in a vertical cross-section of an unconfined aquifer. Two cases are examined: the first involves a homogeneous and isotropic aquifer, while the second comprises a mildly heterogeneous and anisotropic one. The challenges and opportunities arising from this emerging research area are also explored, and essential directions for future research are underscored.