Sequential Gaussian simulation for geosystems modeling: A machine learning approach

Sequential Gaussian Simulation (SGSIM) as a stochastic method has been developed to avoid the smoothing effect produced in deterministic methods by generating various stochastic realizations. One of the main issues of this technique is, however, an intensive computation related to the inverse operation in solving the Kriging system, which significantly limits its application when several realizations need to be produced for uncertainty quantification. In this paper, a physics-informed machine learning (PIML) model is proposed to improve the computational efficiency of the SGSIM. To this end, only a small amount of data produced by SGSIM are used as the training dataset based on which the model can discover the spatial correlations between available data and unsampled points. To achieve this, the governing equations of the SGSIM algorithm are incorporated into our proposed network. The quality of realizations produced by the PIML model is compared for both 2D and 3D cases, visually and quantitatively. Furthermore, computational performance is evaluated on different grid sizes. Our results demonstrate that the proposed PIML model can reduce the computational time of SGSIM by several orders of magnitude while similar results can be produced in a matter of seconds.