## 1 Introduction
Despite the availability of various mathematical, empirical, and physics-based models currently used in the drilling and well construction sector, incidents related to swab and surge pressures continue to occur. The comparisons of field-measured data with the hydraulic well-flowing models showed discrepancies, and the model required a calibration factor based on measured data ([PERSON] et al., 2008) [23]. Simulation studies conducted by [PERSON] et al., 2023 [24] showed that the swab and surge prediction of the models were inconsistent and deviated from each other for the considered experimental setup. In recent years, the application of data-driven modeling has been employed in various sectors, including petroleum drilling. There are several machine learning modeling algorithms. For instance, [PERSON] et al. (2022, 2023) [24; 25] utilized machine learning techniques (i.e., linear regression, multivariable regression (MVR), Random Forest, ANN, long-short-term memory (LSTM), and XGboost models) to predict the tripping and drilling operation's equivalent circulating mud density (ECD), and the results showed satisfactory performance. In the petroleum industry, among others, ANN algorithms have been applied for prediction such as ROP ([PERSON] (2020) [26], [PERSON] (2019) [27]), ECD ([PERSON] (2020) [28], [PERSON] et al., 2021 [24; 25]), drilling speed ([PERSON] et al. (2020) [29]), and drilling-fluid-rheological-parameter real-time prediction ([PERSON] et al. (2018) [30]). In addition, [PERSON] (2024) implemented machine learning to investigate Swell Mitigation [31]. [PERSON] (2023) studied the importance of data integration in Geotechnical Engineering [32]. [PERSON] (2022) deployed machine learning techniques to predict dysfunctional events in drilling and wells [33]. A literature review indicates the application of the Group Method of Data Handling (GMDH) technique across diverse fields. GMDH is an extended version of multivariable regression that contains non-linear interacting terms. Among others, GMDH has been utilized for accurate log interval value estimation ([PERSON] (2014) [34]), permeability prediction by [PERSON] (2019) [35] and [PERSON] (2023) [36], as well as permeability modeling and pore pressure analysis by [PERSON] (2020) [37]. Additionally, GMDH finds applications in cement compressive strength design ([PERSON], 2023 [38]), rock deformation prediction ([PERSON] et al., 2020 [39]), bubble point pressure estimation by [PERSON] (2022) and [PERSON] (2022) [40,41], gas viscosity determination, CO\({}_{2}\) emission modeling ([PERSON] et al., 2020 and 2018 [42,43]), the prediction of CO\({}_{2}\) adsorption by [PERSON] (2019) [44] and [PERSON] (2017) [45], forecasting stock indices, and modeling power and torque as demonstrated by [PERSON] (2015) [46] and [PERSON] (2023) [47], and the prediction of pore pressure by [PERSON] (2023) [48]. The GMDH neural network architecture is not as fully connected as that of the commonly used ANN. The modeling performance of the GMDH network in comparison with that of the ANN model is presented in several publications including [PERSON] et al., 2012 [49]; [PERSON] et al., 2020 [50]; [PERSON] et al., 2015 [46]; [PERSON] et al., 2015 [43]. This study aimed to implement four machine learning algorithms on field drilling data. The first study compared MVR with GMDH to assess the impact of the non-linear interacting features that GMDH has on model prediction. The second study proposed new GMDH-method-generated features that can be utilized as inputs for deep-learning (ANN) modeling, and the networks were fully connected. Then, the newly proposed GMDH-ANN method was compared with a standard ANN that did not include interacting terms. Finally, empirical models were derived from field drilling data by using GMDH and MVR methods.