The accurate forecasting of oil recovery factors is crucial for the effective management and optimization of oil production processes. This study explores the application of machine learning methods, specifically focusing on parallel algorithms, to enhance traditional reservoir simulation frameworks using black oil models. This research involves four main steps: collecting a synthetic dataset, preprocessing it, modeling and predicting the oil recovery factors with various machine learning techniques, and evaluating the model’s performance. The analysis was carried out on a synthetic dataset containing parameters such as porosity, pressure, and the viscosity of oil and gas. By utilizing parallel computing, particularly GPUs, this study demonstrates significant improvements in processing efficiency and prediction accuracy. While maintaining the value of the $R^2$ metric in the range of 0.97, using data parallelism sped up the learning process by, at best, 10.54 times. Neural network training was accelerated almost 8 times when running on a GPU. These findings underscore the potential of parallel machine learning algorithms to revolutionize the decision-making processes in reservoir management, offering faster and more precise predictive tools. This work not only contributes to computational sciences and reservoir engineering but also opens new avenues for the integration of advanced machine learning and parallel computing methods in optimizing oil recovery.

In this work, the construction of adaptive one-dimensional computational grids is considered using a numerical method and physics-informed neural networks (PINNs). The grid adaptation process is described by the diffusion equation, which allows for the redistribution of nodes based on a control function. The numerical method employs an iterative scheme that adjusts the node positions according to the solution gradients, ensuring local refinement in key regions. In the PINN approach, the governing equation is incorporated into the loss function, enabling the neural network model to generate the grid based on physical constraints. To evaluate the performance of both methods, tests are conducted with different control function parameters, and the influence of diffusion coefficients on grid adaptation is analyzed. The results show that the numerical method leads to sharper variations in node spacing, while PINNs produce a smoother grid distribution. A comparative analysis of the deviations between the methods is performed. The obtained data allow for assessing the characteristics of grid adaptation in both approaches and for identifying possible directions for their further application in numerical modeling tasks.

This paper presents an approach to constructing adaptive one-dimensional computational grids using the Beltrami equation and Physics-Informed Neural Networks (PINNs). The main focus is on exploring the potential for precise control of grid node density through the control function ω(s), which allows the grid to adapt to the local features of the problem. The Beltrami equation used, being a key component of the method, regulates the distribution of nodes by modifying the function’s derivatives depending on the values of the control function. The effectiveness of this approach is demonstrated through examples involving one and two regions of node clustering. The results showed that the PINN method combined with the Beltrami equation allows for the creation of computational grids with a high degree of adaptation to given conditions, providing detailed modeling in critical regions. This approach has advantages over traditional numerical methods, as integrating physical laws in the grid construction process minimizes numerical errors and improves modeling accuracy. The use of neural networks offers flexibility in model tuning and the ability to account for complex nonlinear dependencies. The discussion of the results highlights the potential of using PINNs for adaptive grid construction in various fields requiring precise and efficient modeling. In conclusion, this study confirms that the combination of the Beltrami equation and PINNs is a powerful tool for adaptive grid construction, opening new possibilities for numerical modeling of complex physical processes.

Adaptive computational grids improve the accuracy and efficiency of numerical simulations by concentrating nodes in regions of particular interest, but classical adaptation methods based on differential equations are often computationally expensive and geometry-dependent. This study proposes a physics-informed neural network (PINN) framework for generating two-dimensional structured adaptive grids by solving the diffusion equation directly, with grid density governed by a prescribed control function. Two neural architectures were developed and compared: a classical PINN, in which boundary conditions are enforced softly through an additional loss term, and a modified PINN (MPINN), in which Dirichlet boundary conditions are embedded exactly into the network architecture using an approximate distance function (ADF) mask. Both methods were tested on two adaptation scenarios—concentration at a single point and concentration along a line segment—and validated against a reference grid obtained by a finite-difference scheme. The MPINN model reduced the mean root-mean-square error by a factor of between 1.4 and 2.0, depending on the adaptation case, together with improved boundary agreement, symmetry, and interval uniformity. Two further configurations with control functions of a more complex shape, a T-shaped junction and a curve of diagonal sine form, were examined together with a variant in which the boundary nodes are allowed to slide along the boundary while the boundary itself is preserved exactly. In these configurations the classical PINN fails to preserve the domain, whereas both mask-based variants reproduce it by construction. The results demonstrate that embedding boundary conditions architecturally, rather than penalizing their violation in the loss function, substantially improves the accuracy and reliability of PINN-based adaptive grid generation.

In today’s world, data processing and machine learning play a key role in various sectors, including science, industry and technology. As the volume of data increases, the need for effective methods and tools for their analysis increases. Graphics processing units (GPUs) become a necessary element in this process, as they allow complex calculations to be performed in parallel. This article analyzes the efficiency of GPU usage in machine learning. The research covers the use of the RAPIDS libraries (cuMl and cuDF) to perform data analysis and implement machine learning algorithms on the GPU. Alternative machine learning methods, including linear regression and SVM, implemented using the RAPIDS and Scikit-Learn libraries, are also being studied. The presented analysis highlights the advantages of using GPU in training models, especially when working with large amounts of data. The algorithms considered in the study were tested on a dataset created using the Buckley-Leverett mathematical model to predict the oil recovery coefficient. The article demonstrates the importance and potential of using GPUs in machine learning, highlighting key methods that contribute to improving the performance and efficiency of algorithms.