Accounting for uncertainty of variables in data-driven modelling by EPR

The interest of hydroinformatics in data-driven modelling has significantly increased in recent years. Nonetheless, the description of physical phenomenon by reproducing patterns in input-output datasets is unavoidably affected by uncertainties surrounding data. On one hand, the mere maximization of model fit to uncertain data might result into incorrect identification of patterns. On the other hand, the quantification of uncertainty propagation from input variables to data-driven model output is needed for their correct use. This paper proposes the employment of a recent variant of the Evolutionary Polynomial Regression (EPR), named Multi Case Strategy for EPR (MCS-EPR) in order to account for uncertainty of input variables during model development. The resulting MSC-EPR model structures are expected to reflect the “physical” relationship between input variables and outputs, while the variance of regression parameters estimated for multiple realizations of the input dataset is likely to reproduce the propagation of uncertainty from inputs to model output. The analysis encompasses both a theoretical discussion and a numerical example.