Prediction of geoid undulation using approaches based on GMDH, M5 model tree, MARS, GPR, and IDP

This study provides a comprehensive comparison of four different machine learning models including the group method of data handling (GMDH), M5 model tree (M5MT), multivariate adaptive regression spline (MARS), and Gaussian process regression (GPR) for predicting geoid undulation. For the first time, GMDH and M5MT were applied for this purpose. The obtained results were also compared with the classic inverse distance to a power (IDP) interpolation method. In order to assess the consistency of our results, two test sites with different topographic features were used for the evaluation of the models. In constructing the models, the geographic coordinate values and the geoid undulation value were used as inputs and output, respectively. Several statistical indices and rank analysis were used for evaluation of the models. According to the comparative results of all models in both test sites, the GMDH yielded the best performance among the developed models. The M5MT also exhibited acceptable results. Thus, it may be concluded that the proposed GMDH and M5MT have the potential to be alternative models that could assist geoscientists working with the geoid.