# Parsimonious Universal Function Approximator for Elastic and Elasto-Plastic Cavity Expansion Problems

arXiv: https://arxiv.org/abs/2407.19074 · HTML: https://mlsanity.com/paper/2407.19074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Meshless physics-informed deep learning method for three-dimensional solid mechanics](https://mlsanity.com/paper/2012.01547/) (2020)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [Energy-based error bound of physics-informed neural network solutions in elasticity](https://mlsanity.com/paper/2010.09088/) (2020)
- [Deep Learning for One-dimensional Consolidation](https://mlsanity.com/paper/2004.11689/) (2020)
- [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)

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Extreme Learning Machine (PIELM) for Tunnelling-Induced Soil-Pile Interactions](https://mlsanity.com/paper/2510.00698/) (2025)

## Abstract (arXiv)

Cavity expansion is a canonical problem in geotechnics, which can be described by partial differential equations (PDEs) and ordinary differential equations (ODEs). This study explores the potential of using a new solver, a physics-informed neural network (PINN), to calculate the stress field in an expanded cavity in the elastic and elasto-plastic regimes. Whilst PINNs have emerged as an effective universal function approximator for deriving the solutions of a wide range of governing PDEs/ODEs, their ability to solve elasto-plastic problems remains uncertain. A novel parsimonious loss function is first proposed to balance the simplicity and accuracy of PINN. The proposed method is applied to diverse material behaviours in the cavity expansion problem including isotropic, anisotropic elastic media, and elastic-perfectly plastic media with Tresca and Mohr-Coulomb yield criteria. The results indicate that the use of a parsimonious prior information-based loss function is highly beneficial to deriving the approximate solutions of complex PDEs with high accuracy. The present method allows for accurate derivation of solutions for both elastic and plastic mechanical responses of an expanded cavity. It also provides insights into how PINNs can be further advanced to solve more complex problems in geotechnical practice.