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

• URL: http://arxiv.org/abs/2607.12271v1
• Date: Tue, 14 Jul 2026 02:17:30 GMT
• Title: A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground
• Abstract summary: We propose a physics-informed neural network to approximate a universal corrector with respect to a single borehole with unit heat extraction rate.<n>We perform numerical tests to exhibit the effectiveness of the proposed method based on three different analytical models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

Related papers

• Linearized PINN with pretrained nonlinear layers [48.01541150431857]
  lPINN is a reduced-order neural basis method for forward and inverse differential equations.<n>We evaluate lPINN on forward and inverse problems for the advection-diffusion equation, Burgers' equation, and the nonlinear pendulum equation.
  arXiv  Detail & Related papers  (2026-09-14T02:18:00Z)
• Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devices [0.0]
  We develop an inverse Physics-Informed Neural Network framework to infer the dependence of the scrape-off layer (SOL) perpendicular heat conductivity on plasma density and temperature.<n>The framework is validated using synthetic data generated from a prescribed conductivity function.<n>A scan in the number of plasma profiles used for training and the number of radial measurement positions per profile identifies a practical trade-off between reconstruction accuracy and data availability.
  arXiv  Detail & Related papers  (2026-09-10T14:40:32Z)
• Differential Learning for Robust Prediction of Thermal Stability with Application to Energetic Materials [0.0]
  We train neural networks to predict relative differences between pairs of molecules.<n>This approach reduces sensitivity to systematic experimental errors and achieves >85% accuracy in ranking compounds by thermal stability.<n>Our results demonstrate that learning relative properties rather than absolute values offers a practical solution for modeling noisy experimental data.
  arXiv  Detail & Related papers  (2026-08-24T22:28:56Z)
• Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems [48.470700002941136]
  Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization.<n> physics-informed neural networks (PINNs) have emerged as a flexible alternative.<n>We present a fair comparison of adjoint optimization and PINNs for PDE-constrained inverse problems.
  arXiv  Detail & Related papers  (2026-06-10T17:07:09Z)
• Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces [42.33765011920294]
  We introduce a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal solvers.<n>Our approach employs a single neural field where a unified shared backbone is conditioned on signal-specific latent variables.<n>We validate our approach through applications in seismic travel-time modeling of 2D, 3D, and spherical benchmark datasets.
  arXiv  Detail & Related papers  (2025-05-21T21:29:18Z)
• Finite Operator Learning: Bridging Neural Operators and Numerical Methods for Efficient Parametric Solution and Optimization of PDEs [0.0]
  We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. We can parametrically solve partial differential equations in a data-free manner and provide accurate sensitivities. Our study focuses on the steady-state heat equation within heterogeneous materials.
  arXiv  Detail & Related papers  (2024-07-04T21:23:12Z)
• Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths [41.94295877935867]
  We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling.<n>We compare two different approaches to obtain thermal Green functions.<n>We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations.
  arXiv  Detail & Related papers  (2024-06-17T18:00:07Z)
• A Physics-driven GraphSAGE Method for Physical Process Simulations Described by Partial Differential Equations [2.1217718037013635]
  A physics-driven GraphSAGE approach is presented to solve problems governed by irregular PDEs. A distance-related edge feature and a feature mapping strategy are devised to help training and convergence. The robust PDE surrogate model for heat conduction problems parameterized by the Gaussian singularity random field source is successfully established.
  arXiv  Detail & Related papers  (2024-03-13T14:25:15Z)
• Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations [0.0]
  We present a method that employs physics-informed deep learning techniques for solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions.
  arXiv  Detail & Related papers  (2024-01-04T17:01:54Z)
• Uncertainty quantification and out-of-distribution detection using surjective normalizing flows [46.51077762143714]
  We propose a simple approach using surjective normalizing flows to identify out-of-distribution data sets in deep neural network models. We show that our method can reliably discern out-of-distribution data from in-distribution data.
  arXiv  Detail & Related papers  (2023-11-01T09:08:35Z)
• PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations [14.044012646069552]
  We present a new category of physics-informed neural networks called physics informed embedding generative adversarial network (PI-VEGAN) PI-VEGAN effectively tackles forward, inverse, and mixed problems of differential equations. We evaluate the effectiveness of PI-VEGAN in addressing forward, inverse, and mixed problems that require the concurrent calculation of system parameters and solutions.
  arXiv  Detail & Related papers  (2023-07-21T01:18:02Z)
• On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform [62.997667081978825]
  We describe the low-temperature optical conductivity as a function of frequency for a quantum-mechanical system of electrons that hop along a polymer chain. Our goal is to show vias how the interband conductivity of this system behaves as the smallest energy bandgap tends to close.
  arXiv  Detail & Related papers  (2022-09-26T23:17:39Z)
• A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures [68.8204255655161]
  It is shown that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches. It is shown, that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches.
  arXiv  Detail & Related papers  (2021-10-26T07:02:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.