This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the PINN utilizing the continuous symmetry data inherent in PDEs, which is called the symmetry-enhanced Physics-Informed Neural Network. This innovative approach combines artificial neural networks (ANNs) integrating physical equations, which provide enhanced efficiency and accuracy when modeling various complex processes related to physics with a symmetric and asymmetric nature. The presented mathematical model, based on the system of Euler equations, has been carefully implemented using Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In this research, a comparative and comprehensive analysis was carried out comparing the outcomes obtained using the symmetry-enhanced PINN method and those from conventional computational fluid dynamics (CFD) approaches. The analysis highlighted the advantages of the symmetry-enhanced PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing the computation time, demonstrating its capacity as a revolutionary modeling tool. The estimated results derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulations has the potential to improve the integrity of our energy infrastructure and utilization of gas resources, contributing to advancing our understanding of symmetry principles in nature. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations. The numerical data covered the physics of the process related to the modeling of high-pressure gas flows in pipelines with regard to density, velocity and pressure, where the PINN model was able to outperform the classical CFD method for velocity by 170% and for pressure by 360%, based on $L_{\infty }$ values.

The article describes the IoT infrastructure, the hardware of the IoT system, considers the issue of security of the chosen LoRa data transmission technology. Data was received from sensors for gas, temperature and humidity, atmospheric pressure, as well as the location of the end device. At the same time, the standardized security features of the selected LoRa technology for transmitting data from sensors to the server were investigated. The article deals with LoRa bi-directional secure communication line, the security function requires devices/end devices to be configured through the LoRa gateway. Security research is devoted to the development of a security mechanism to increase its resilience. The payload was formed with a hash of the last bytes, and the entire payload was encrypted with AES for integrity and confidentiality. A method for assessing and visualizing atmospheric air pollution is given on the example of the city of Almaty, Kazakhstan. The process of numerical modeling of the study of emissions of harmful substances into the atmosphere is based on a mathematical model formed by the system of Navier-Stokes equations, consisting of the continuity equation, as well as the equations of motion and the k-epsilon turbulence model. To test the numerical methods for processing mixing and chemical reactions, a test problem was chosen – a jet in a transverse flow. Three-dimensional numerical simulation has been implemented. The use of the Internet of Things (IoT) and the acquisition of big data made it possible to simultaneously observe the concentrations of several pollutants in the atmosphere, calculate this concentration and analyze the state of the surface air layer. Modeling allows forecasting the possible concentration of pollutants in certain areas at certain times of the year.

This study develops a mathematical model for soil moisture diffusion, addressing the inverse problem of determining both the diffusion coefficient and the variation coefficient in a nonlinear moisture transfer equation. The model incorporates specific boundary and initial conditions and utilizes experimentally measured moisture values at a boundary point as input data. An iterative method, based on an explicit gradient scheme, is introduced to estimate the soil parameters. The initial boundary value problem is discretized, leading to a difference analog and the formulation of a conjugate difference problem. Iterative formulas for calculating the unknown parameters are derived, with a priori estimates ensuring the convergence of the iterative process. Additionally, the research establishes the convergence of the numerical model itself, providing a rigorous foundation for the proposed approach. The study also emphasizes symmetry in moisture calculations, ensuring consistency regardless of the calculation direction (from right to left or left to right) and confirming that moisture distribution remains symmetric within specified intervals. This preservation of symmetry enhances the model’s robustness and accuracy in parameter estimation. The numerical simulations were successfully conducted over a 7-day period, demonstrating the model’s reliability. The discrepancy between the numerical predictions and experimental observations remained within the margin of measurement error, confirming the model’s accuracy.