# A Deep Learning Approach for Predicting Two-dimensional Soil Consolidation Using Physics-Informed Neural Networks (PINN)

arXiv: https://arxiv.org/abs/2205.05710 · HTML: https://mlsanity.com/paper/2205.05710/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 9 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Deep Learning for One-dimensional Consolidation](https://mlsanity.com/paper/2004.11689/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems](https://mlsanity.com/paper/2401.05439/) (2024)
- [Parsimonious Universal Function Approximator for Elastic and Elasto-Plastic Cavity Expansion Problems](https://mlsanity.com/paper/2407.19074/) (2024)
- [Physics-Informed Extreme Learning Machine (PIELM) for Tunnelling-Induced Soil-Pile Interactions](https://mlsanity.com/paper/2510.00698/) (2025)

## Abstract (arXiv)

Soil consolidation is closely related to seepage, stability, and settlement of geotechnical buildings and foundations, and directly affects the use and safety of superstructures. Nowadays, the unidirectional consolidation theory of soils is widely used in certain conditions and approximate calculations. The multi-directional theory of soil consolidation is more reasonable than the unidirectional theory in practical applications, but it is much more complicated in terms of index determination and solution. To address the above problem, in this paper, we propose a deep learning method using physics-informed neural networks (PINN) to predict the excess pore water pressure of two-dimensional soil consolidation. In the proposed method, (1) a fully connected neural network is constructed, (2) the computational domain, partial differential equation (PDE), and constraints are defined to generate data for model training, and (3) the PDE of two-dimensional soil consolidation and the model of the neural network is connected to reduce the loss of the model. The effectiveness of the proposed method is verified by comparison with the numerical solution of PDE for two-dimensional consolidation. Using this method, the excess pore water pressure could be predicted simply and efficiently. In addition, the method was applied to predict the soil excess pore water pressure in the foundation in a real case at Tianjin port, China. The proposed deep learning approach can be used to investigate the large and complex multi-directional soil consolidation.