Hybrid PINN Model Simulates Geothermal Heat Exchangers in Heterogeneous Soil

Researchers have developed a novel hybrid model combining analytical methods with a parametric physics-informed neural network (PINN) to simulate geothermal heat exchangers (BHEs) operating within heterogeneous underground environments. This framework addresses several key challenges in subsurface thermal modeling. Firstly, it cleverly removes the problematic singularity associated with BHEs by integrating established analytical line source models, simplifying the problem for the neural network. Secondly, the model explicitly incorporates the learning of gradient thermal conductivity, allowing the PINN to effectively parametrize and understand the varying thermal properties of the soil. Thirdly, a significant innovation is the use of a learned correction factor, which acts as an efficient universal corrector. This correction compensates for the difference between the actual heterogeneous solution and an idealized homogeneous approximation, leveraging superposition principles to enhance accuracy and generalizability. The PINN is trained to approximate this universal corrector for a single borehole with a unit heat extraction rate, minimizing a physics-informed and data-anchored loss function. Numerical tests confirm the method's effectiveness, demonstrating its ability to accurately model complex thermal problems in heterogeneous soil, offering a more efficient and robust simulation tool for geothermal energy applications.