An improved method of groundwater model structural uncertainty analysis

Gaussian Process Regression (GPR) is a supervised learning algorithm based on Bayesian theory, which is widely used in model structural uncertainty analysis based on data-driven method (DDM). In this study, it is usually assumed that the physical parameters and hyperparameters are independent and identified jointly, which will lead to parameter compensation. In this paper, a two-stage based DDM method is proposed to quantify the model structural errors, and two case studies are used to compare and analyze the results of parameter identification and model prediction with considering the model structural errors (joint calibration based DDM and two-stage based DDM) and without considering the model structural errors. The results show that when the parameters are identified directly without considering the model structural errors, the parameters will be overfitted and compensate the model structural errors, thereby affecting the model prediction performance. When considering the model structure deviation based on DDM, the independence assumption of physical parameters and hyperparameters will affect the parameter estimation results. The proposed two-stage based DDM method does not assume that the physical parameters and hyperparameters are independent, and can reduce parameter overfitting caused by the independence assumption of physical parameters and hyperparameters, portraying more accurate structural errors and effectively improving the model prediction performance.