Accurately predicting the filtration volume (FV) in drilling fluid (DF) is crucial for avoiding drilling problems such as a stuck pipe and minimizing DF impacts on formations during drilling. Traditional FV measurement relies on human-centric experimental evaluation, which is time-consuming. Recently, machine learning (ML) proved itself as a promising approach for FV prediction. However, existing ML methods require time-consuming input variables, hindering the semi-real-time monitoring of the FV. Therefore, employing radial basis function neural network (RBFNN) and multilayer extreme learning machine (MELM) algorithms integrated with the growth optimizer (GO), predictive hybrid ML (HML) models are developed to reliably predict the FV using only two easy-to-measure input variables: drilling fluid density (FD) and Marsh funnel viscosity (MFV). A 1260-record dataset from seventeen wells drilled in two oil and gas fields (Iran) was used to evaluate the models. Results showed the superior performance of the RBFNN-GO model, achieving a root-mean-square error (RMSE) of 0.6396 mL. Overfitting index (OFI), score, dependency, and Shapley additive explanations (SHAP) analysis confirmed the superior FV prediction performance of the RBFNN-GO model. In addition, the low RMSE (0.3227 mL) of the RBFNN-NGO model on unseen data from a different well within the studied fields confirmed the strong generalizability of this rapid and novel FV prediction method.