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

TL;DR

This paper introduces a physics-informed neural network framework for efficiently solving three-dimensional Terzaghi consolidation problems, demonstrating high accuracy in forward and inverse soil settlement predictions with over 99% accuracy.

Contribution

The paper presents a novel PINNs framework tailored for 3D consolidation equations, including specific loss functions and tuning strategies, outperforming traditional numerical methods in accuracy and efficiency.

Findings

PINNs achieved over 99% accuracy in simulations.

The framework effectively handles noisy data in inverse problems.

Compared favorably with traditional numerical methods.

Abstract

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