基于物理信息神经网络能量桩周土体热–力耦合高效求解方法

doi:10.3724/1000-6915.jrme.2025.0559

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摘要为研究能量桩周土体的热–力耦合作用，基于物理信息神经网络（PINNs）方法，提出一种高效的无网格数值求解模型。该模型将热扩散方程与Navier应力平衡方程作为物理约束，以控制方程残差的形式嵌入损失函数中，从而确保训练过程严格遵循物理守恒定律。与有限元数值计算结果对比验证表明：所构建的PINNs热–力耦合模型的最优网络配置为4层隐藏层，每层50个神经元以及Tanh激活函数，其温度场和位移场预测的最大相对误差分别为0.53%和5.72%。在优化策略方面，Adam与L-BFGS混合优化使总损失值降至4.42×10－4，较单一使用Adam和L-BFGS优化分别提升了51.52%与15.33%。此外，拉丁超立方采样策略显著提升了模型精度，其温度预测平均相对误差较均匀采样与随机采样分别降低了77.03%与76.81%。引入迁移学习框架后，该模型在新工况下仅需9.35%的计算成本即可达到与完整重新训练相当的精度，整体计算效率较传统有限元方法提升了16.55%。研究成果可为地下工程热–力耦合问题研究提供一种新的兼具物理严谨性和计算高效性的求解方案。

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	王志良1
	肖智桓1
	申林方1*
	刘海明1
	李泽1
	李淼2

关键词 ：桩基础, 物理信息神经网络, 能量桩, 热&ndash, 力耦合作用, 深度学习, 迁移学习

Abstract：To investigate the thermo-mechanical coupling for soil surrounding energy pile, an efficient mesh-free numerical model based on the physics-informed neural networks (PINNs) method is proposed. The model incorporates the heat diffusion equation and Navier stress equilibrium equation as physical constraints by embedding the residuals of the governing equations into the loss function, thereby ensuring that the training process strictly adheres to physical conservation laws. Validation against finite element simulation results indicates that the optimal configuration of the proposed PINNs model consists of four hidden layers with 50 neurons per layer and the Tanh activation function, achieving maximum relative errors of only 0.53% and 5.72% for the temperature and displacement fields, respectively. In terms of optimization strategy, the hybrid Adam+L-BFGS optimizer reduces the total loss to 4.42×10??, improving performance by 51.52% and 15.33% compared with using Adam and L-BFGS individually. Moreover, the Latin hypercube sampling strategy significantly enhances model accuracy, reducing the average relative temperature prediction error by 77.03% and 76.81% compared with uniform and random sampling, respectively. With the introduction of a transfer learning framework, the model achieves comparable accuracy to full retraining under new working conditions at only 9.35% of the computational cost, improving overall computational efficiency by 16.55% compared with the traditional finite element method. The proposed approach provides a new solution for studying thermo-mechanical coupling problems in underground engineering, combining physical rigor with high computational efficiency.

Key words： pile foundations physics-informed neural networks (PINNs) energy pile thermo-mechanical coupling deep learning transfer learning

引用本文:

王志良1，肖智桓1，申林方1*，刘海明1，李泽1，李淼2. 基于物理信息神经网络能量桩周土体热–力耦合高效求解方法[J]. 岩石力学与工程学报, 2026, 45(3): 903-917.
WANG Zhiliang1, XIAO Zhihuan1, SHEN Linfang1*, LIU Haiming1, LI Ze1, LI Miao2. An efficient thermo-mechanical coupling solution for soil surrounding energy pile based on physics-informed neural networks. , 2026, 45(3): 903-917.

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https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0559 或 https://rockmech.whrsm.ac.cn/CN/Y2026/V45/I3/903

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