Physics-informed neural networks for solving steady-state temperature field in artificial ground freezing

Artificial ground freezing (AGF) is a widely used technique for soil stabilization and waterproofing. Numerous studies have been devoted to solving the heat transfer problems in AGF while encountering limitations in handling complex geometries and boundary conditions and being computationally intensive. Recently, using machine learning methods to predict temperature fields has gained attention, demonstrating the potential to achieve higher accuracy than conventional models. However, these methods are typically limited by the need for large, labeled datasets, which are time-consuming and difficult to obtain. In this study, we address these challenges by applying physics-informed neural networks (PINNs) to solve the steady-state heat transfer problem in AGF, focusing on the temperature distribution around a single freezing pipe. By embedding the heat conduction equation into the loss function, PINNs reduce the need for extensive labeled data. To enhance accuracy and efficiency, transfer learning is employed, and results are compared against the finite element method. Results show that PINNs achieve high accuracy, particularly in larger domains with moderate temperature gradients, while providing competitive performance in more complex configurations involving steeper gradients. This approach offers a promising alternative for modeling temperature fields in geotechnical applications, with implications for reducing computational costs in AGF design.