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The knowledge of reservoir permeability determination is increasingly important in petroleum engineering. Understanding the alteration of the abovementioned parameter as a dynamic characteristic of formations helps the characterization of reservoir rock. The existing models available for permeability determination are mainly developed for sandstone reservoir; therefore, a great challenge is in the prediction of permeability in carbonate heterogeneous rock. The current study addresses the application of Gaussian Process Regression (GPR), a state-of-the-art machine learning algorithm, in estimating permeability of carbonate reservoirs. This Bayesian network offers various benefits including non-linearity and multi-dimensionality. A widespread source of data pertinent to four deposits of Vuktyl'skiy, central Asia, Kuybyhev, and Orenburg was adopted from literature. The data set includes water saturation, effective porosity, and pore specific surface area parameters in association with absolute rock permeability as the target. Four different Kernels of Matérn, rational quadratic, exponential, and squared exponential are utilized as the covariance functions of the GPR network. A wide variety of the visualizations and statistical parameters are prepared to assess the potential of the established models in permeability estimation. Finally, it is demonstrated that the GPR (Matérn) gives the highest precision with Mean Magnitude Relative Error (MMRE) and Adjusted R-squared equal to 38% and 0.98, respectively. Besides, the applied sensitivity analysis reveals that porosity and irreducible water saturation have the lowest and the highest absolute impact values on permeability estimation. The applicability and validity of the developed models are also demonstrated by means of the so-called Williams' method for outliers detection. At last, it is worthwhile mentioning that the created new methods in this study can be good nominees for permeability determination in characterizing the heterogeneous carbonate reservoirs. Image 1 • A kernel-based probabilistic modeling approach, namely GPR method, is used for model development. • A comprehensive literature databank is undertaken for permeability of heterogeneous carbonate reservoirs. • Several statistical measures and illustrations are used to assess the model performance. • GPR model with Matern' kernel indicates the best agreement with the real permeabilities as compared to other models. • GPR model can be a potential candidates for predicting the permeability of heterogeneous carbonate reservoirs. [ABSTRACT FROM AUTHOR]