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Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems

arXiv 2401.05439 ↗First posted 8 Jan 2024cs.LG cs.CEcited by 1

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Abstract (arXiv)

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

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 30 of its 80 references that are in the map. First posted on arXiv 8 Jan 2024.

Builds on

30 of 80 references.

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18 more
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Citing papers per year: 2025: 1.

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  1. 2025Physics-Informed Extreme Learning Machine (PIELM) for Tunnelling-Induced Soil-Pile Interactionscited by 0