Bayesian-informed DNN and ensemble learning for predicting soil water characteristic curves from easily measurable parameters

Soil-water characteristic curve (SWCC) represents one of the important properties describing the hydraulic characteristics of unsaturated soil, with extensive application value in geotechnical engineering, but the experimental process for obtaining SWCC is complex and time-consuming. This research proposes a prediction framework based on Bayesian-informed machine learning for SWCC applicable to different soil types, using easily measurable soil parameters. This model uses quantified particle size distribution, bulk density, and saturated water content as input features, and employs Bayesian-Markov Chain Monte Carlo methods to inversely derive Fredlund-Xing (FX) model parameters as output features. Deep Neural Network (DNN) and stacking models based on ensemble learning of five regressors were constructed to establish the prediction framework. Results show that both DNN and stacking models effectively capture complex nonlinear relationships between the three easily measured soil parameters and FX parameters, demonstrating good prediction accuracy. The stacked model shows better prediction results, with R² exceeding 0.94 for all three parameters, outperforming the DNN model (R² = 0.93). Through feature engineering and SHAP (Shapley Additive Explanations)-based feature sensitivity analysis, the relationships between input features and the three FX model parameters were physically interpreted, providing physical interpretability for the machine learning models. The prediction method offers a new approach for fast and accurate acquisition of SWCC, expanding the application of machine learning methods in the field of unsaturated soils.