## 1 Introduction
As reservoir complexity grows and data collection expands exponentially, there is an urgent need for more efficient computational techniques that not only accelerate processes but also enhance the simulation accuracy. Machine learning (ML) has become an indispensable tool in earth sciences and represents a significant advancement, providing robust tools for the efficient and precise exploration of mineral resources. These methods are employed for tasks such as dimensionality reduction, classification, regression, and clustering, which are crucial for accurate mineral potential mapping [17; 18]. ML has emerged as a fundamental instrument in the field of oil reservoir simulations, providing a wide array of applications that improve both efficiency and precision. One primary application is in the estimation of original oil in place (OOIP), where ML algorithms, particularly artificial neural networks (ANNs), are used to predict reserves with high accuracy, even when the data are insufficient [19]. Additionally, ML techniques are employed in reservoir production optimization, where advanced algorithms like ANNs optimize the cumulative oil recovery by evaluating various field development scenarios and well placements [20]. In geomechanical modeling, ML predicts the rock mechanical properties using conventional well logging data, thus reducing the need for costly dipole sonic logs [21]. ML also aids in optimizing the polymer injection processes by predicting the oil recovery factor using regression algorithms and ANNs, which are trained on extensive synthetic datasets [22]. In underground natural gas storage, ML models optimize parameters such as well positioning to maximize the gas delivery while minimizing the CO\({}_{2}\) production [23]. Surrogate proxy models created using ML techniques like XGBoost and MLP are used to estimate the net present value (NPV) of the reservoirs under various operating conditions, thereby aiding in decision-making for well placements and production strategies [24]. Furthermore, ML accelerates the reservoir simulation processes by providing fast and competent results that mimic traditional simulators,thus reducing the computational time and costs [25]. The integration of ML with numerical methods enhances the precision of partial differential equation discretization in reservoir simulations, leading to rapid convergence and high computational efficiency [26]. ML also automates and accelerates reservoir characterization, production forecasting, and well test interpretation, making these processes more efficient and cost-effective [27]. Lastly, deep learning models with neural operators in Fourier space significantly reduce the computational time required for direct numerical simulations, enabling faster and more accurate predictions for reservoir management [28]. The potential of ML in reservoir management includes property prediction, oil recovery factor prediction, production optimization, enhanced oil recovery testing, and performance metrics analysis, demonstrating its versatility and effectiveness in the oil and gas industry. However, the application of parallel machine learning algorithms--those utilizing multiple processors simultaneously for enhanced efficiency--to tackle the black oil problem remains underexplored. This gap is significant, given parallel computing's potential to significantly reduce processing times and manage large-scale data more effectively, particularly in reservoir simulations. There are numerous parallelization methods for modern computing systems, including MPI, OpenMP, TBB (Threading Building Blocks), and LMK (Linux Kernel Module) for CPUs, as well as OpenCL and CUDA for GPUs. However, for our purposes, it was decided to focus on two well-established technologies: MPI and the RAPIDS cuML library based on Nvidia CUDA [29; 30; 31; 32; 33; 34; 35]. These tools were chosen for their high performance and ease of integration into our machine learning workflow.