*5.2. Testing the Developed Machine Learning Models*

The performance of the developed machine learning models in evaluating the Estatic for the testing dataset, which was collected from the same training formation used to developed machine learning models (i.e., from Well-A), was evaluated. As indicated in Figure 6, all machine learning models predicted Estatic with very high accuracy. M-FIS predicted Estatic for the testing dataset with AAPE and R of 0.09% and 0.999992, respectively, FNN model predicted Estatic with AAPE of 0.85% and R of 0.999311, then SVM model which estimated Estatic with an AAPE and R of 0.62% and 0.999813, respectively, and the ANN estimated Estatic with AAPE of 1.46% and R of 1.000000. Visual check of the actual and estimated Estatic of the testing data set also confirmed the high accuracy of the machine learning models, as indicated by the good matching between the actual and estimated Estatic.

**Figure 6.** Actual and estimated Estatic for the testing dataset collected from Well-A.

### *5.3. Validation of the Developed Machine Learning Models*

The machine learning models' accuracy was finally validated using 38 data points collected from another sandstone formation in Well-B. Figure 7 compares the actual core derived and estimated Estatic using the developed machine learning for the validation data set. The results in Figure 7 confirmed that all machine learning models predicted Estatic with very high accuracy. This figure also confirmed that M-FIS technique is the best among the others on estimating Estatic for the validation data set, where the developed M-FIS predicted Estatic with AAPE of 1.56% and R of 0.999, followed by SVM model which predicted Estatic with AAPE of 2.03% and R of 0.999, then FNN model which estimated Estatic with AAPE of 2.54% and R of 0.997, and the least accurate model was the ANN which predicted Estatic with AAPE of 3.80% and R of 0.991.

**Figure 7.** Core-derived and predicted Estatic for the validation dataset collected from Well-B.

A visual check of the actual and estimated Estatic of the validation data set also confirmed the high accuracy of all machine learning models considered in this work, as confirmed by the good matching between the estimated and core derived Estatic. A continuous profile of Estatic along the drilled sections of Well-B was obtained using the machine learning models. This is not possible to achieve by conducting laboratory work only. The confidence intervals for the validation data were ± 0.574, ± 0.804, ± 0.843, and ± 0.877, with a confidence level of 99% for M-FIS, SVM, ANN, and FNN models, respectively.

Figure 8 compares the AAPE for the calculated Estatic for training, testing, and validation datasets using the different machine learning models. This figure confirms that the developed M-FIS model overperformed the other machine learning models in predicting Estatic for the training, testing, and validation datasets in terms of AAPE. M-FIS predicted Estatic with the lowest AAPE of 1.56 %, while the AAPE for the SVM, FNN, and ANN were 2.03, 2.54, and 3.80, respectively.

**Figure 8.** Comparison of the AAPE for the training, testing, and validation datasets for all machine learning models.

Out of the results of training, testing, and validation data and 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 models accuracy, we conclude that the four models are equally adequate to estimate Estatic using only the conventional well log used in this study. Nevertheless, we recommend using the M-FIS model as it is the best-performed model for estimating Estatic for the training, testing, and validation data.

The machine learning models developed in this work are very helpful for the petroleum engineers and petroleum industry since they could positively improve Estatic estimation, therefore, enabling petroleum engineers and geoscientists to construct the earth geomechanical map and to evaluate the wellbore stability condition, the reservoir compaction, hydraulic fracturing, and the formation control [1,3].

#### **6. Conclusions**

Four machine learning techniques were applied in this study to develop models for estimating Estatic for sandstone formations, these machine learning techniques were ANN, FNN, M-FIS, and SVM. The machine learning models were trained to evaluate Estatic based on conventional well log data of the RHOB, DTs, and DTc. The machine learning models were trained and tested based on data gathered from sandstone formation in Well-A and then the developed models were validated on unseen data

collected from a sandstone formation in Well-B. The outcomes of this work confirmed the high accuracy of all machine learning models, and M-FIS models overperformed all others in estimating Estatic for training, testing, and validation data sets. For the validation data, M-FIS predicted Estatic with a very low AAPE of 1.56% and R of 0.999. The high accuracy of the developed machine learning models was also confirmed by visual comparison of the estimated and actual Estatic.

**Author Contributions:** Conceptualization, S.E; data preparation, S.E., and A.A.M.; models development, A.A.M.; results analysis, A.A.M.; writing—original draft preparation, A.A.M.; writing—review and editing, S.E., and D.A.S.; supervision, S.E. All authors have read and agreed to the published version of the manuscript.

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