Modeling Transient Groundwater Flow in Unconfined Aquifers Under Dynamic Conditions Using Physics‐Informed Neural Networks

Abstract Deep learning neural networks (DLNNs) hold great potential for modeling groundwater flow, but their performance depends on data availability. Physics‐informed neural networks (PINNs) help to reduce the reliance of DLNNs on data by integrating physical laws into the training process. This approach is increasingly used in applications related to groundwater flow. However, most applications remain limited to steady‐state conditions in confined aquifers. Training PINNs for unconfined aquifers and under dynamic conditions is challenging due to the nonlinearity of the governing equations and the large number of required collocation points. The applicability of PINNs in such a case is still poorly investigated. The main objective of this paper is to fill this gap by focusing on the treatment of time derivatives in PINNs. Thus, three PINNs approaches based on continuous time (i.e., standard PINNs), discrete time and time decomposition are adapted and compared. A comprehensive explanation of the principles of discrete PINNs for modeling groundwater flow is provided. The performance of these three approaches is investigated using several test cases involving variable boundary conditions or pumping rates. The results demonstrate the superiority of the discrete‐time approach in both accuracy and training efficiency. The advantages of this approach become more pronounced as the complexity of the velocity and pressure head fields increases. This approach can be 10 times more efficient than standard PINNs in training time because it allows for optimizing the number of collocation points and reducing both the number of training parameters and training epochs.