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

翻译：受物理控制方程约束的神经网络的兴起引发了深度学习研究的新趋势，即物理信息神经网络（Physics-Informed Neural Networks, PINNs）。然而，利用PINNs求解高维问题仍然是一个重大挑战，空间复杂度给求解大规模多方向问题带来了困难。本文提出了一种新颖的PINNs框架，能够快速预测不同条件下多个三维太沙基固结案例。同时，引入了不同案例下的损失函数，并强调了它们在三维固结问题中的差异。介绍了针对三维固结问题的PINNs框架调优策略。随后，测试了PINNs的性能，并与正问题中采用的传统数值方法进行了比较，识别了固结系数以及反问题中含噪声数据的影响。最后，总结并展示了PINNs的三维模拟结果，结果表明，与真实值相比，正问题和反问题的准确率均超过99%。这些结果具有良好精度，可用于土体沉降预测，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。关键词：三维太沙基固结；物理信息神经网络；正问题；反问题；土体沉降