Fig. 1 Schematic of applied methodology in this paper Artificial intelligence methods can learn the pattern of data and use multiple inputs, but previous attempts were merely based on one input without any learning (just sim- ple regression). Also, this paper applies not only one way but also 15 distinct methods for this purpose. Moreover, the results of these methods are compared to finding the most proper model. The final result of the best machine learning method is then compared with the previously pre- sented equations. The depth, T,,,,, S;/TOC, and HI param- eters are applied as inputs of constructed models by 15 machine learning methods of decision tree (DT), random forest (RF), support vector machine (SVM), group method of data handling (GMDH), radial basis function (RBF), multilayer perceptron (MLP), multilayer perceptron couple with grasshopper optimization algorithm (MLP + GOA), bat algorithm (MLP+ BAT), particle swarm optimization algorithm (MLP+ PSO), and genetic algorithm (MLP+ GA) as well as adaptive neuro-fuzzy inference system (ANFIS), ANFIS + GOA, ANFIS + BAT, ANFIS+PSO and ANFIS + GA for VR determination. Then, the accuracy of all methods was compared through four statistical param- eters of average absolute relative deviation (AARD), coeffi- cient of determination (R2), root mean square error (RMSE), Fig. 2. Location map of studied wells in the Persian Gulf As mentioned in this paper, the required data for predict- ing VR are depth, T,,,,, 5,/TOC, and HI. To that end, 54 data sets of these aforementioned data are extracted from a broad area of the Persian Gulf as can be seen in Fig. 2. The Persian Gulf, as the most significant foreland basin Table 1 Minimum, maximum, and average values of selected inputs and output data Fig. 3 Simplified stratigraphic column of studied formations After selecting proper and complete data, 54 Rock-Eval pyrolysis data (depth, T,,,,,, S;/TOC, and HI) belong to ten oil fields in the Iranian sector of the Persian Gulf (Fig. 2) were extracted (Mashhadi et al. 2015). Minimum, maxi- mum, and average values of selected data are summarized in Table 1. Twenty-one samples belong to Pabdeh Forma- tion, whereas contributions of Gurpi Formation, Ahmadi member, and Kazhdumi Formation are 6, 4, and 23 samples, respectively. In this paper, data of depth, T,,,,, S,/TOC, and HI are considered as inputs of constructed models, and VR is the output. Data normalizing, which improves the perfor- mance of constructed models, has been done through the below equation: Fig.4 Schematic of DT workflow 2 hidden layers was selected. As is evident, the efficiency of these types of networks depends on the number of neurons in each layer. To that end, several MLP networks with dif- ferent numbers of neurons were constructed, and then their performances were analyzed by mean square error. This procedure is illustrated in Fig. 10. As shown, the structure with three neurons in the first in the second hidden layer c situation. Since determining parameters requires several ca hidden layer and four neurons an be considered as the best the optimum values of MLP culations, which takes a lot of time, for increasing efficiency, other parameters are derived from the previous study (Sabal flowchart is presented in Fig. used MLP network with two Table 4. h et al. 2019a). Also, the MLP 11. The characteristics of the hidden layers are presented in Fig.5 Schematic of SVM workflow Table 2 Values of GMDH parameters The smart hybrid system of ANFIS is the conflation of fuzzy logic and artificial neural network, and this feature makes AN FIS an effective tool and powerful strategy with high accuracy and less time for goals of systems recogni- tion, time series prediction, function approximation, simula- tion of non Additional inear systems, etc. (Jang 1993; Mir et al. 2018). information on ANFIS parameters is listed in Table 5. It must be noted that ANFIS parameters have been determined through previous research (Sabah et al. 2019a) and trial and error approach. Furthermore, the algorithm and the flowchart’s architecture are shown in Figs. 12 and 13, respectively. Table 3 Properties of RBF network Fig. 8 Schematic of RBF workflow Fig.9 Schematic of RF workflow Table 4 Architecture parameters of MLP network Fig. 12 Simplified structure of the ANFIS algorithm As a general procedure, constructed models by different aforementioned methods must be compared. To that end, statistical parameters are considered as appropriate tools for appraising the performance of defined models. In this paper, four parameters of average absolute relative devia- tion (AARD), coefficient of determination (R7), root mean square error (RMSE), and standard deviation (SD) have been employed for a com plete comparison of 15 distinct developed models and selection of the most precise methods for vitrinite reflectance prediction. Equations of these statistical parameters are expressed as fol OWS: Four above indicators are calculated for all implemented models, and graphical results for three categories of train data, test data, and total data are illustrated in Figs. 19, 20, Fig. 15 Schematic of BAT workflow Fig. 17 Schematic of PSO workflow Fig. 18 The plot of the relationship between inputs and output values Fig. 19 Comparison of devel- oped models on the basis of the AARD statistical parameter computed for these experimental equations and summa- rized in Table 8. For better understanding, the statisti- cal parameters of the decision tree are also listed in this table. As seen, the DT method with the lowest amounts of AARD, RMSE, SD, and the highest value of R? is the most approach (as the most precise machine learning method) with depth are illustrated in Fig. 27. Empirical equations perform weakly for vitrinite reflectance prediction. Table 7 Statistical parameters values for all constructed models Conclusions HI values were selected for vitrinite reflectance predic- tion. Decision tree (DT), support vector machine (SVM), group method of data handling (GMDH), radial basis function (RBF), random forest (RF), multilayer percep- tron (MLP), MLP+GOA, MLP+ BAT, MLP+PSO and MLP+GA, adaptive neuro-fuzzy inference system (ANFIS), ANFIS + GOA, ANFIS + BAT, ANFIS + PSO, Vitrinite reflectance values have been predicted by using machine learning approaches for the first time in this paper. For this purpose, several Rock-Eval parameters were used to construct machine learning models. For this purpose, in addition to depth, T S,/TOC, and max? Fig. 23 An implemented tree for vitrinite reflectance prediction. Statistical information and vitrinite reflectance values are shown in blue rectan- gles and orange ellipsoids, respectively Fig. 24 Relative deviation plot of the decision tree model Fig. 25 Experimental data of vitrinite reflectance and prediction val- ues by DT Table8 The calculated statistical parameters for DT method and empirical equations of 6-9 acceptable, whereas the decision tree can be considered as the most accurate method, which possesses the lowest rela- tive deviation between measured and predicted vitrinite reflectance values. A comparison between the decision tree and previously proposed equations for vitrinite reflectance prediction indicates that the machine learning approach performs more accurately than empirical equations. Fig. 26 Predicted values of Ro by DT versus experimental values for both train and test datasets
