The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with PINNs is still a substantial challenge, the space complexity brings difficulty to solving large multidirectional problems. In this paper, a novel PINN framework to quickly predict several three-dimensional Terzaghi consolidation cases under different conditions is proposed. Meanwhile, the loss functions for different cases are introduced, and their differences in three-dimensional consolidation problems are highlighted. The tuning strategies for the PINNs framework for three-dimensional consolidation problems are introduced. Then, the performance of PINNs is tested and compared with traditional numerical methods adopted in forward problems, and the coefficients of consolidation and the impact of noisy data in inverse problems are identified. Finally, the results are summarized and presented from three-dimensional simulations of PINNs, which show an accuracy rate of over 99% compared with ground truth for both forward and inverse problems. These results are desirable with good accuracy and can be used for soil settlement prediction, which demonstrates that the proposed PINNs framework can learn the three-dimensional consolidation PDE well. Keywords: Three-dimensional Terzaghi consolidation; Physics-informed neural networks (PINNs); Forward problems; Inverse problems; soil settlement

提出了一种新颖的基于物理信息的神经网络（PINNs）框架，用于快速预测不同条件下的几个三维Terzaghi固结情况，并引入了不同情况下的损失函数，在三维固结问题中突出了它们的差异。介绍了三维固结问题中PINNs框架的调优策略，并将其性能与前向问题中采用的传统数值方法进行了测试和比较，确定了固结系数和逆问题中噪声数据的影响。最后，通过针对三维固结问题的模拟总结和展示了PINNs的结果，与地面实况相比，准确率超过99％，在正向和逆向问题上均表现出理想的准确性，可用于土壤沉降预测，证明了所提出的PINNs框架能够很好地学习三维固结偏微分方程。

基于物理信息的深度学习解决三维Terzaghi固结方程：正向和反向问题