*3.1. Training the AI Models*

The AI models considered in this work (TSK-FIS, M-FIS, FNN, and SVM) were trained to optimize their design parameters, the optimum design parameters of the AI models are summarized earlier in Table 2. Figure 3 compares the predictability of the four optimized AI models for the training data sets, as shown in Figure 3. The number of data used to train every AI model are different. As explained earlier, the training to testing data ratio is considered during the models optimization process, and based on this optimization, the number of training data that maximize predictability of every model is selected.

**Figure 3.** Comparison of measured and estimated TOC using (**a**) TSK-FIS, (**b**) M-FIS, (**c**) FNN, and (**d**) SVM for the training data sets.

Figure 3 shows that the TSK-FIS model predicted the TOC for the training data set with the highest accuracy compared to other models, with AAPE of 7.12% and R of 0.968. M-FIS comes second with AAPE and R of 7.48% and 0.962, followed by the FNN model with AAPE of 8.05% and R of 0.936, and finally the SVM model with AAPE and R of 9.75%, and 0.933, respectively. The visual check of the plots confirms a high accuracy of the four AI models in estimating the TOC for the training data set.

Cross-plot of Figure 4 compares the measured and estimated TOC for the training data set. The narrow scattering of the points indicates the predictability of the models; TSK-FIS model is the

highest with R<sup>2</sup> = 0.937, then M-FIS model with R<sup>2</sup> = 0.926, followed by FNN model with R2 = 0.876, and finally SVM with the lowest R2 of 0.871.

**Figure 4.** Cross-plot of the measured and estimated TOC using (**a**) TSK-FIS, (**b**) M-FIS, (**c**) FNN, and (**d**) SVM for the training data set.

#### *3.2. Testing the AI Models*

The predictability of the four AI models, developed in this study, is then tested using data collected from the Barnett shale formation. The number of the testing data points is selected based on the optimization process as mentioned earlier.

Figure 5 compares the predictability of the AI models to evaluate the TOC for the testing data sets. Visually, the four plots indicate similar predictability for the four models, with minor differences. Considering the AAPE and R M-FIS model is the highest with 11.10% and 0.933, followed by TSK-FIS model with 11.20% and 0.918, then FNN model with 11.29% and 0.905, and finally SVM model with 11.45%, and 0.931 respectively.

The cross-plot in Figure 6 presents the correlation between measured and estimated TOC for the testing data set. The plots indicate high correlation with R2 equal 0.870, 0.867, 0.842, and 0.818 for M-FIS, SVM, TSK-FIS, and FNN models, respectively.

**Figure 5.** Comparison of measured and estimated TOC using (**a**) TSK-FIS, (**b**) M-FIS, (**c**) FNN, and (**d**) SVM for the testing data sets.

**Figure 6.** Cross-plot of the measured and estimated TOC using (**a**) TSK-FIS, (**b**) M-FIS, (**c**) FNN, and (**d**) SVM for the testing data sets.

#### *3.3. Validating the AI Models*

The AI model's validation was completed using unseen data collected from the Devonian shale formation. The total number of core derived TOC data collected from Devonian shale are 22 data points, out of these data, only 20, 19, 19, and 15 were found to fit within the range of the training data that is used to develop TSK-FIS, M-FIS, FNN, and SVM models, respectively. The range for the training data are summarized in Table 1. Based on the AAPE and R results as indicated in Figure 7, FNN model was the best model with AAPE of 12.02% and R of 0.879, followed by M-FIS model with AAPE and R of 13.18 and 0.875, then SVM with AAPE and R of 14.52% and 0.860, and finally TSK-FIS model with AAPE of 15.62% and R of 0.832 respectively. As shown in Figure 7, all AI models are highly accurate compared to Wang et al. [12] sonic- and density-based models, Wang sonic-based model (WSBM) predicted the TOC with AAPE of 34.58% and R of 0.806, while Wang density-based model (WDBM) predicted TOC with AAPE, and R of 49.04% and 0.469, respectively.

**Figure 7.** Comparison of measured and estimated TOC using (**a**) TSK-FIS, (**b**) M-FIS, (**c**) FNN, (**d**) SVM, (**e**) WSBM, and (**f**) WDBM for the validation data sets.

From the the results of training, testing, and validation data, considering the similarity of the results of the evaluation parameters (AAPE and R), and taking into consideration that adding or omitting a few points may change the highest-to-lowest order of the parameters, we conclude that the four models are equally adequate to estimate the TOC using only the conventional well log used in this study. Nevertheless, we recommend using the FNN model as it is the best-performed model on the validation data.

#### **4. Conclusions**

In this study, four artificial intelligence (AI) models based on Takagi-Sugeno-Kang fuzzy interference system, Mamdani fuzzy interference system, functional neural network, and support vector machine are developed to estimate the total organic carbon (TOC) using conventional well logs of deep resistivity, gamma-ray, sonic transit time, and bulk density. The models are developed and tested using data collected from Barnett shale and then validated using unseen data from Devonian shale. The optimized AI models showed a high predictability of TOC for both formations evaluated in this study. The four models are equally adequate to estimate the TOC using the well log used in this study. Nevertheless, for the validation (unseen) data considered in this study, the FNN model overperformed other models in predicting the TOC, with the lowest AAPE and the highest R, compared with other

techniques. All AI models over-performed Wang models, which are recently developed to evaluate the TOC for Devonian formation.

**Author Contributions:** Conceptualization, S.E., A.A. and A.A.M; methodology, A.A.M. and M.A.; validation, A.A.M., S.E. and M.A.; formal analysis, A.A.M. and A.Z.A; data preparation, A.A.M.; models preparation, A.A.M., A.A. and A.Z.A.; writing—original draft preparation, A.A.M.; writing—review and editing, S.E., A.Z.A. and M.A.; visualization, A.Z.A. and A.A.; supervision, S.E. and A.A.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
