TS-PIELM: Time-Stepping Physics-Informed Extreme Learning Machine Facilitates Soil Consolidation Analyses

2025-06-10

AI Summary

Conventional physics-informed neural networks (PINNs) suffer from low accuracy and slow training when applied to soil consolidation analysis. Method: This paper proposes a time-stepping physics-informed extreme learning machine (TS-PIELM), which partitions the consolidation process into temporal subdomains and employs a single-layer ELM architecture with randomly assigned, fixed hidden-layer weights; output weights are computed analytically via linear least squares, eliminating gradient-based optimization. The novel time-stepping strategy mitigates numerical stiffness arising from steep-gradient partial differential equations. Contribution/Results: Evaluated on the one-dimensional Terzaghi consolidation problem, TS-PIELM achieves over 1000× speedup in computational efficiency and reduces relative error by more than two orders of magnitude compared to standard PINNs. These advances significantly enhance both the accuracy and efficiency of physics-informed machine learning for geotechnical engineering applications.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Humans and AI: Human-in-the-loop Machine Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Accuracy and efficiency of the conventional physics-informed neural network (PINN) need to be improved before it can be a competitive alternative for soil consolidation analyses. This paper aims to overcome these limitations by proposing a highly accurate and efficient physics-informed machine learning (PIML) approach, termed time-stepping physics-informed extreme learning machine (TS-PIELM). In the TS-PIELM framework the consolidation process is divided into numerous time intervals, which helps overcome the limitation of PIELM in solving differential equations with sharp gradients. To accelerate network training, the solution is approximated by a single-layer feedforward extreme learning machine (ELM), rather than using a fully connected neural network in PINN. The input layer weights of the ELM network are generated randomly and fixed during the training process. Subsequently, the output layer weights are directly computed by solving a system of linear equations, which significantly enhances the training efficiency compared to the time-consuming gradient descent method in PINN. Finally, the superior performance of TS-PIELM is demonstrated by solving three typical Terzaghi consolidation problems. Compared to PINN, results show that the computational efficiency and accuracy of the novel TS-PIELM framework are improved by more than 1000 times and 100 times for one-dimensional cases, respectively. This paper provides compelling evidence that PIML can be a powerful tool for computational geotechnics.

Problem

• Improves accuracy and efficiency of soil consolidation analysis
• Overcomes PINN limitations with TS-PIELM approach
• Enhances training speed using ELM and linear equations

Innovation

• Time-stepping divides consolidation into intervals
• Single-layer ELM replaces fully connected network
• Random fixed input weights enhance efficiency