发表机构
Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究以钻孔换热器为奇异源的非均质土壤热问题，开发参数化物理信息神经网络，利用解析线源模型等特性，通过温度变化分解等步骤将原始问题重述，经训练得到通用校正器，数值测试验证了该方法的有效性。
AI 中文摘要
本文开发了一种参数化物理信息神经网络，用于解决以钻孔换热器（BHEs）为奇异源的非均质土壤热问题。该框架有三个新特性：一是用解析线源模型自然消除奇点；二是利用热导率的显式公式实现对热导率参数化的物理信息学习；三是通过叠加原理将学习到的校正用作高效通用校正器。首先介绍温度变化分解，将非均质响应近似转换为校正，排除狄拉克函数奇点并捕获整体热传递以利于神经网络有效训练。接着将原始问题重新表述为服从齐次初始条件的控制校正扩散或平流-扩散方程，用线性变化热导率模拟土壤非均质性。提出物理信息神经网络近似单位热提取率下单孔的通用校正器，通过在自适应选择的训练点上对采样电导率参数评估的物理信息和数据锚定损失函数进行训练。还将源的位置指示函数作为网络特征输入，发现有助于处理局部信息。基于三种不同解析模型进行数值测试，展示了该方法的有效性。
英文摘要
Accurate and efficient prediction of subsurface temperature fields is essential for the design and operation of borehole heat exchanger (BHE) systems. Here we develop a parametric hybrid analytical and physics-informed neural network (PINN) framework for long-term multi-BHE simulations in heterogeneous underground. The method analytically extracts the singular line source response and enables the effective training of neural correction associated with subsurface heterogeneity. An explicit parametrization of the thermal conductivity allows physics-informed learning of a single feedforward neural network to generalize across different subsurface conditions. By formulating the correction in borehole-centered relative coordinates, the learned correction can be reused as a universal corrector through spatial and temporal superposition principles. Numerical experiments based on the infinite line source (ILS), finite line source (FLS) and moving finite line source (MFLS) models show that the hybrid method outperforms analytical approximations with stable accuracy over long simulation horizons and achieves orders-of-magnitude speedups over traditional solvers. The proposed framework therefore combines the efficiency of analytical models with the ability of numerical methods to capture heterogeneous subsurface physics, providing a fast and accurate approach for repeated long-term simulation of multi-BHE systems.
Comments30 pages, 16 figures
