# Physics-Informed Extreme Learning Machine (PIELM) for Tunnelling-Induced Soil-Pile Interactions

arXiv: https://arxiv.org/abs/2510.00698 · HTML: https://mlsanity.com/paper/2510.00698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations](https://mlsanity.com/paper/1907.03507/) (2019)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Deep learning of free boundary and Stefan problems](https://mlsanity.com/paper/2006.05311/) (2020)
- [Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2205.06948/) (2022)
- [A Deep Learning Approach for Predicting Two-dimensional Soil Consolidation Using Physics-Informed Neural Networks (PINN)](https://mlsanity.com/paper/2205.05710/) (2022)
- [Application of Physics-Informed Neural Networks for Forward and Inverse Analysis of Pile-Soil Interaction](https://mlsanity.com/paper/2212.08306/) (2022)
- [Physics-informed extreme learning machine for Terzaghi consolidation problems and interpretation of coefficient of consolidation based on CPTu data](https://mlsanity.com/paper/2506.08381/) (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)

## Abstract (arXiv)

Physics-informed machine learning has been a promising data-driven and physics-informed approach in geotechnical engineering. This study proposes a physics-informed extreme learning machine (PIELM) framework for analyzing tunneling-induced soil-pile interactions. The pile foundation is modeled as an Euler-Bernoulli beam, and the surrounding soil is modeled as a Pasternak foundation. The soil-pile interaction is formulated into a fourth-order ordinary differential equation (ODE) that constitutes the physics-informed component, while measured data are incorporated into PIELM as the data-driven component. Combining physics and data yields a loss vector of the extreme learning machine (ELM) network, which is trained within 1 second by the least squares method. After validating the PIELM approach by the boundary element method (BEM) and finite difference method (FDM), parametric studies are carried out to examine the effects of ELM network architecture, data monitoring locations and numbers on the performance of PIELM. The results indicate that monitored data should be placed at positions where the gradients of pile deflections are significant, such as at the pile tip/top and near tunneling zones. Two application examples highlight the critical role of physics-informed and data-driven approach for tunnelling-induced soil-pile interactions. The proposed approach shows great potential for real-time monitoring and safety assessment of pile foundations, and benefits for intelligent early-warning systems in geotechnical engineering.