The experimental design of well cement with durable compressive strength (CS) is challenging and time-consuming. The current research predicts CS using the enhanced group method of data handling via a modified Levenberg-Marquardt algorithm (GMDH-LM) with experimental data. Class F fly ash (CFFA) is used as a supplementary material to cement at various proportions. Experimental tests of CS, thermogravimetric (TG) analysis, rheology, and scanning electron microscopy (SEM) are applied. Experimental findings revealed that the addition of fly ash (FA) enhances CS with curing time as an outcome of pozzolanic action. CS for 20% FA reinforcement after curing for 28 days was 42.95 MPa, compared with 41.53 MPa for 50%. This indicates that a higher addition of FA lowers CS. The rheological findings revealed that FA enhanced the viscosity of the cement slurry. The SEM images demonstrated that the incorporation of CFFA with cement modified the contexture of hardened cement. Cement, water, oilwell cement (OWC), curing time, dispersant, and FA were assigned as input variables for GMDH-LM while CS from the experimental analysis was set as output. Machine learning (ML) findings indicated that GMDH-LM can effectively estimate the CS of OWC. GMDH-LM performed better than backpropagation neural network (BPNN), support vector machine (SVM), and normal GMDH models in predicting CS; it provided higher linearity during training as GMDH-LM gave R2 = 0.958, GMDH = 0.946, SVM = 0.925, BPNN = 0.897, and the least loss functions of mean square error (MSE) = 0.238, MSE = 1.685, MSE = 2.567, and MSE = 4.032, respectively. Similarly, good results were ascertained during testing GMDH-LM provided R2 = 0.928, GMDH = 0.907, SVM = 0.895, BPNN = 0.878, and the lowest loss functions of MSE = 0.304, MSE = 2.650, MSE = 3.494, and MSE = 5.678, respectively. Therefore, the comparative results of all experiments and predictions reveal that GMDH-LM can be deployed as an advanced approach for the estimation of cement hydration in oil and gas wells.

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