Hai‐Sui Yu

Xiao-Xuan Chen, Pin Zhang, Hai-Sui Yu et al.

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.

He Yang, Fei Ren, Hai-Sui Yu et al.

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.