A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

2026-07-13

AI Summary

This study addresses the challenges of singularity and computational efficiency in modeling heat conduction within heterogeneous subsurface media containing borehole ground heat exchangers. To overcome these issues, the authors propose an efficient hybrid approach that integrates an analytical line-source model with a physics-informed neural network (PINN). By leveraging the superposition principle, the temperature field is decomposed into a homogeneous analytical solution and a heterogeneous correction term. A universal corrector network is then constructed to implicitly account for the Dirac delta heat source singularity without explicit treatment. The method further incorporates explicit gradient-based thermal conductivity parameterization and spatial indicator functions as input features to enable physics-guided, adaptive learning. Numerical experiments on three representative heterogeneous models demonstrate that the proposed framework achieves high accuracy and strong generalization while significantly improving the efficiency of geothermal response simulations.

Abstract

In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed. There are three novel features in the present framework; namely, (i) the singularity is naturally removed by using analytical line source models; (ii) using the explicit formulation for gradient thermal conductivity enables physics-informed learning of the parametrization featuring the conductivity; (iii) the learned correction is utilized as an efficient universal corrector via superposition principles. We first introduce the decomposition of the temperature change and transform the approximation of the entire heterogeneous response to the correction compensating the difference between the practical solution and idealized homogeneous approximation. In such a way, the delta function singularity is excluded and the bulk heat transfer is captured for the sake of facilitating the effective training of the neural network. The original problem is then reformulated as a governing correction diffusion or advection-diffusion equation subject to a homogeneous initial condition. The linearly varying thermal conductivity is used to model the soil heterogeneity. We propose a physics-informed neural network to approximate a universal corrector with respect to a single borehole with unit heat extraction rate. As a result, the network is trained by minimizing the physics-informed and data-anchored loss function that is evaluated for sampled conductivity parameters on adaptively selected training points. In addition, we include the location indicator function regarding the source as a feature input of network and find that it helps the network to process the local information. We perform numerical tests to exhibit the effectiveness of the proposed method based on three different analytical models.

Problem

• geothermal heat exchangers
• heterogeneous subsurface
• singular sources
• thermal conductivity
• subsurface simulation

Innovation

• physics-informed neural network
• heterogeneous thermal conductivity
• singularity removal
• universal corrector
• borehole heat exchanger