## 7 Conclusions  
The study establishes hybrid machine learning (HML) models to predict the filtration volume (FV) of water-based drilling fluids (WBDF) in semi-real-time, using only two easily and regularly measured parameters, the drilling fluid density (FD) and the Marsh funnel viscosity (MFV), as inputs. Two HML models are developed that are associated with the radial basis function neural network (RBFNN) and multiple extreme learning machine (MELM) algorithms and are optimized with the recently developed growth optimizer (GO). To construct predictive models for the FV, data from seventeen wells drilled in two fields in Iran (1260 data records) were randomly divided into training and testing sets, utilizing a 90/10 training/testing separation ratio determined through sensitivity analysis. Outlying data were detected and eliminated from the process using a Gaussian process regression (GPR)-Mahalanobis distance (MD)-cross-validation technique. The control parameters of the HML model were fine-tuned using the GO algorithm, and these algorithms were then applied to the training data. The testing data subsets were then evaluated with the trained models. The models' FV prediction performances were scrutinized with scoring techniques, robustness analysis, and overfitting assessments. The best-performing model, based on these evaluations, was further interpreted using Shapley additive explanations (SHAP) and partial dependency (PDP) analysis. The generalizability and prediction performance of the optimal model was further validated by applying it to predict the FV for unseen data from another well from one of the studied fields. This study's key findings are:  
A two-parameter prediction model is developed, for the first time, to accurately estimate the drilling fluids' FV in semi-real-time. A total of forty-eight data records were identified and eliminated as outliers through the GPR-MD-cross-validation technique. The HML model, RBFNN-GO, exhibited the best FV prediction performance, achieving an RMSE of 0.519 mL (training subset) and 0.6396 mL (testing subset). The RBFNN-GO model achieved the lowest overfitting index of 0.0327, identifying it as the most generalizable of the four models evaluated. Figure 16: Workflow diagram demonstrating how the configured HML models can be applied in the DF well-site laboratory to assist the drilling crew with FV semi-real-time monitoring and decision making. Score analysis confirmed the superior FV prediction performance of the RBFNN-GO model, and noise robustness testing showed it to be the most robust of the models evaluated. SHAP analysis of the trained RBFNN-GO model revealed that both the FD and the MFV significantly influenced the FV predictions of DFs, with the MFV exerting somewhat greater influence than the FD. PDP of the relative influence of the FD and the MFV on the RBFNN-GO model identified that the MFV and the FD exert complex and non-linear inter-relationships that influence the model's FV predictions. Those relationships show that the model achieves its minimum FV predictions at the low FD values within the MFV range of 40 to 60 and its maximum FV predictions at the low MFV values, especially when the FD value is maximized. Applying the RBFNN-GO model to ninety-nine unseen data points from another well in the studied fields demonstrated its high predictive accuracy, with an RMSE of 0.3227 mL and an R\({}^{2}\) of 0.9624. These results confirm that the model is highly effective at accurately predicting the FV for other wells in the studied fields. Reliable and regular estimation of the FV offers the potential to avoid formation damage by minimizing the mud filtration invasion and to reduce the risk of differential stuck drill-pipe incidents by minimizing the filter cake thickness. The developed model improves upon the existing FV prediction models by making it possible to conduct semi-real-time monitoring of the FV during drilling operation with data inputs measured routinely at the well-site. Conceptualization, S.D., M.M. and M.A.-S.; data curation, S.D. and M.M.