A gated recurrent unit model to predict Poisson's ratio using deep learning

Static Poisson's ratio (νs) is crucial for determining geomechanical properties in petroleum applications, namely sand production. Some models have been used to predict νs; however, the published models were limited to specific data ranges with an average absolute percentage relative error (AAPRE) of more than 10%. The published gated recurrent unit (GRU) models do not consider trend analysis to show physical behaviors. In this study, we aim to develop a GRU model using trend analysis and three inputs for predicting νs based on a broad range of data, νs (value of 0.1627–0.4492), bulk formation density (RHOB) (0.315–2.994 g/mL), compressional time (DTc) (44.43–186.9 μs/ft), and shear time (DTs) (72.9–341.2 μs/ft). The GRU model was evaluated using different approaches, including statistical error analyses. The GRU model showed the proper trends, and the model data ranges were wider than previous ones. The GRU model has the largest correlation coefficient (R) of 0.967 and the lowest AAPRE, average percent relative error (APRE), root mean square error (RMSE), and standard deviation (SD) of 3.228%, −1.054%, 4.389, and 0.013, respectively, compared to other models. The GRU model has a high accuracy for the different datasets: training, validation, testing, and the whole datasets with R and AAPRE values were 0.981 and 2.601%, 0.966 and 3.274%, 0.967 and 3.228%, and 0.977 and 2.861%, respectively. The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges, which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.