arXiv subjects

Hai-Sui Yu

Publications and source records attributed to Hai-Sui Yu.

6 recordsLinked to original sources

arXiv2025

Physics-Informed Extreme Learning Machine (PIELM): Opportunities and Challenges

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a comprehensive summary or review of PIELM is currently unavailable, we would like to take this opportunity to share our perspectives and experiences on this promising research direction. We can see that many efforts have been made to solve ordinary/partial differential equations (ODEs/PDEs) characterized by sharp gradients, nonlinearities, high-frequency behavior, hard constraints, uncertainty, multiphysics coupling, and interpretability. Despite these encouraging successes, many pressing challenges remain to be tackled, which also provides opportunities to develop more robust, interpretable, and generalizable PIELM frameworks for scientific and engineering applications.

cs.LG↗

arXiv2025

General Fourier Feature Physics-Informed Extreme Learning Machine (GFF-PIELM) for High-Frequency PDEs

Conventional physics-informed extreme learning machine (PIELM) often faces challenges in solving partial differential equations (PDEs) involving high-frequency and variable-frequency behaviors. To address these challenges, we propose a general Fourier feature physics-informed extreme learning machine (GFF-PIELM). We demonstrate that directly concatenating multiple Fourier feature mappings (FFMs) and an extreme learning machine (ELM) network makes it difficult to determine frequency-related hyperparameters. Fortunately, we find an alternative to establish the GFF-PIELM in three main steps. First, we integrate a variation of FFM into ELM as the Fourier-based activation function, so there is still one hidden layer in the GFF-PIELM framework. Second, we assign a set of frequency coefficients to the hidden neurons, which enables ELM network to capture diverse frequency components of target solutions. Finally, we develop an innovative, straightforward initialization method for these hyperparameters by monitoring the distribution of ELM output weights. GFF-PIELM not only retains the high accuracy, efficiency, and simplicity of the PIELM framework but also inherits the ability of FFMs to effectively handle high-frequency problems. We carry out five case studies with a total of ten numerical examples to highlight the feasibility and validity of the proposed GFF-PIELM, involving high frequency, variable frequency, multi-scale behaviour, irregular boundary and inverse problems. Compared to conventional PIELM, the GFF-PIELM approach significantly improves predictive accuracy without additional cost in training time and architecture complexity. Our results confirm that that PIELM can be extended to solve high-frequency and variable-frequency PDEs with high accuracy, and our initialization strategy may further inspire advances in other physics-informed machine learning (PIML) frameworks.

cs.LG↗

arXiv2025

Physics-informed extreme learning machine for Terzaghi consolidation problems and interpretation of coefficient of consolidation based on CPTu data

This paper conducts a preliminary study to investigate the feasibility of a physics-informed extreme learning machine (PIELM) for solving the Terzaghi consolidation equation and interpreting the coefficient of consolidation of soil from piezocone penetration tests (CPTu). In the PIELM framework, the target solution is approximated by a single-layer feed-forward extreme learning machine (ELM) network, instead of the deep neural networks typically employed in physics-informed neural networks (PINNs). Physical laws and measured data are integrated into a loss vector, which is minimized via least squares methods during ELM training. As a result, training efficiency is significantly improved by avoiding the gradient-descent optimisation commonly used in PINNs. The performance of PIELM is evaluated using three forward-problem case studies. Notably, a time-stepping strategy is incorporated into the PIELM framework to alleviate sharp gradients caused by inconsistent initial and boundary conditions. This paper further applies PIELM to estimate the soil consolidation coefficient, given that initial distributions of excess water pressure are often unavailable in CPTu dissipation tests (conducted following the pauses of penetration). By combining physical laws (excluding initial conditions) with measured data (i.e., excess pore-water pressure at the probe surface), the results demonstrate that PIELM is an effective tool for interpreting CPTu dissipation tests, owing to its ability to fuse data with physical constraints. This study contributes to the interpretation of consolidation coefficients from CPTu dissipation tests, particularly in scenarios where initial distributions of excess water pressure are not prior-known.

physics.geo-ph↗

arXiv2025

Cylindrical cavity expansion analysis under partially drained conditions for normalisation of excess water pressure in CPTU

Cone tip resistance and excess water pressure (EWP) measured by piezocone penetration tests (CPTU) may be significantly affected by the partially drained effect in soils with intermediate permeability. To capture this effect, the paper proposes a straightforward, hydro-mechanical coupling solution for cylindrical cavity expansion under partially drained conditions. The mechanical behaviour of soils is modelled using the elastoplastic Tresca model and water flow within porous soils is assumed to obey Darcys law. Two partial differential equations (PDEs) are established in the elastic and plastic zones, respectively, transforming the cavity expansion analysis into a typical Stefan problem with dynamic boundary conditions (i.e. a moving boundary at the elastoplastic interface). An approximate solution for the PDEs is derived by leveraging the variable transformation method. Based on the new solution, a novel normalised penetration rate is defined considering the rigidity index of soils, with which a unique backbone curve for CPTU is found. Finally, the backbone curve is compared with a database comprising 109 in-situ experimental tests, 101 centrifuge modelling tests, and numerical simulation results. The proposed solution may provide a useful theoretical tool for interpreting the consolidation coefficient of fine-grained soils from the penetration stage of multi-rate CPTU, which can enhance the interpretation reliability for CPTU dissipation tests.

physics.geo-ph↗

arXiv2024

Poromechanical solution for one-dimensional large strain consolidation of modified cam clay soil

A theoretical model describing the one-dimensional large strain consolidation of the modified Cam Clay soil is presented in this paper. The model is based on the Lagrangian formulation, and is capable of featuring the variability of soil compressibility (inherently so due to the direct incorporation of the specific Cam Clay plasticity model) and permeability, as well as the impact of overconsolidation ratio. The derivation starts from the establishment of the incremental stress-strain relations for both purely elastic and elastoplastic deformations under one-dimensional compression condition, and thereafter the coefficients of compressibility/volume change that are essential to the consolidation analysis. The governing partial differential equation is then neatly deduced in conjunction with the continuity and equilibrium conditions for the soil, with the vertical effective stress being the privileged unknown to be solved for. Subsequently, semi-analytical solution to the developed rigorous poroelastoplastic large strain consolidation model is obtained and verified with the ABAQUS finite element numerical results. Parametric analyses are finally provided to investigate in detail the influences of the soil overconsolidation ratio, large strain configuration, and the variability of the soil permeability on the calculated one-dimensional consolidation response.

physics.geo-ph↗

arXiv2024

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

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.

cs.CE↗