Uncertainty quantification of deep learning techniques for predicting V s from CPTu

This study investigates four uncertainty quantification-integrated deep learning techniques for developing CPTu-Vs correlations. Three techniques – naïve conformal prediction, deep ensemble, and Monte Carlo dropout – are incorporated within a traditional deep neural network (DNN) framework. A fourth approach adopts a probabilistic framework based on Bayesian neural networks (BNNs). These techniques are applied to a multi-site seismic piezocone test (SCPTu) database comprising both onshore and offshore sites. Comparative analyses assess model accuracy, predictive uncertainty, and data coverage for individual SCPTu profiles and for the full dataset, followed by an evaluation of generalisation performance. Results indicate that deep ensemble and Monte Carlo dropout produce relatively narrow uncertainty bounds, leading to inadequate data coverage of 43% and 56%, respectively, within a 95% confidence interval. Naïve conformal prediction attains the target coverage but yields overly conservative estimates due to its inherent assumptions. BNNs provide balanced performance, offering moderate uncertainty bounds that encompass 71% of observed measurements, thereby evidencing their robustness. For individual SCPTu profiles, higher predictive accuracy is generally associated with lower uncertainty and higher coverage. Poor predictive performance is generally attributed to specific site conditions, including rapid soil stratigraphy transitions and silty soil layers. Furthermore, BNNs demonstrate superior generalisation compared to DNN-based techniques.