Polynomial response surface-informed neural network for implicit slope reliability analysis and uncertainty quantification

In slope reliability analysis, surrogate models are usually designed to replace the computationally expensive performance functions. For slope reliability problems considering high dimensional simulation of soil spatial variability, the surrogate model must be constructed using sufficient sampling points in order to cover the high dimension domain of model parameters, potentially making its robustness sensitive to the sample size. This paper proposes a novel surrogate modelling framework, the PRS-informed NN (alternative to the physics-informed neural network, PINN), which integrates a polynomial response surface (PRS, representing a small-scale physical law indicator) with a neural network surrogate model (NN, representing a large-scale model performance) to enhance the modelling performance across various sample sizes and reduce uncertainty. Based on the Karhunen-Loeve expansion technique, the dimension of variables involved in random field discretization is firstly reduced, simplifying the computation for probability of slope failure (P_f). The PRS that plays a role of basic physical law of slope stability model, is integrated into the neural network by adjusting the training loss function. The feasibility of the proposed method is demonstrated through a synthetic slope model and a real-world slope case study. Results show that the proposed framework improves the accuracy of neural network surrogate models, especially with smaller sample sizes. At last, both aleatory and epistemic uncertainties in the surrogate modelling are quantified, followed by a detailed discussion of the confidence interval for the P_f estimation.