A Comparative Study of MARS, GEP, and GMDH Methods for Modeling Soil Thermal Conductivity

Abstract

The present study used three well-known white-box data-driven models, including multivariate adaptive regression splines (MARS), gene expression programming (GEP), and group method of data handling (GMDH), for generating explicit formulas for the prediction of thermal conductivity of the soil $(\lambda )$. Therefore, 40 soil samples and three input variables, such as moisture content $(\omega )$, porosity $(n)$, and the natural density of soil $(\rho )$, were used to predict $\lambda$. The performance of the proposed formulas was assessed via statistical indicators such as the determination of coefficient (R²), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Statistical criteria have shown that all proposed models provided almost identical results. However, the MARS model was marginally more accurate than the GEP and GMDH models. In addition, the error measures of MARS with RMSE = 0.021, MAE = 0.018, and MAPE = 1.191% were slightly more accurate than GA-ANN (RMSE = 0.030, MAE = 0.025, and MAPE = 1.750%) that reported in the previous study for estimation of $\lambda$. However, the prominent feature of the suggested white-box data-driven models compared to black-box models such as ANN is to provide explicit equations for estimating $\lambda$.