In this paper, a physics-informed neural network containing natural gradient descent is proposed to solve the boundary value problem of the Poisson equation. Machine learning methods used in solving partial differential equations are an alternative to the finite element method. Traditional numerical methods for solving differential equations are not capable of solving arbitrary problems of mathematical physics with equivalent efficiency, unlike machine learning methods. The loss function of the neural network is responsible for the accuracy of solving initial and boundary value problems of partial differential equations. The more efficiently the loss function is minimized, the more accurate the resulting solution is. The most traditional optimization algorithm is adaptive moment estimation, which is still used in deep learning today. However, this approach does not guarantee achieving a global minimum of the loss function. We propose to use natural gradient descent with the Dirichlet distribution which increase the accuracy of solving the Poisson equation.

Keywords: natural gradient descent, Poisson equation, Fisher matrix, finite element method, neural networks

The paper presents a new approach to assessing the level of contamination with heavy metals of the soil-like fraction from landfills using Monte Carlo simulation using the example of landfills located within the borders of Volgograd.It was found that with a probability of 36.2%, the contamination level of a soil-like fraction from the landfill located in the Voroshilovsky district will correspond to moderately hazardous, and with a probability of 63.8%, hazardous. It is economically justified to isolate a soil-like fraction with a low level of pollution to detoxify it and further use it in the territory reclamation. For a soil-like fraction from landfill located in the Traktorozavodsky district, the pollution level was determined as extremely hazardous and hazardous with a probability of 87.1% and 3.1%, respectively. It is shown that a useful and usable part cannot be isolated from a soil-like fraction. A soil-like fraction must be neutralized and placed at waste disposal facilities.The presented approach is a useful instrument for pollution level assessment of a soil-like fraction, which can increase the accuracy of an estimate and the management effectiveness of a soil-like fraction during landfill development.

Keywords: landfill, soil-like fraction, heavy metals, pollution level, Monte Carlo method, modeling

The relevance of the topic of the article is due to the fact that currently there is no linking of the calendar plan to the schedule for the development of capital investments. The principle of constructing a schedule for the development of capital investments is proposed, which ensures the uniformity and proportionality of the use of financial resources. Schedules for the development of capital investments are constructed, each schedule for the development of capital investments corresponds to an image describing the change in the absolute value of the profitability of the investment and construction project. The use of a mathematical apparatus describing the movement of a material point can be used in the development of investment schedules and calendar plans for construction. The construction of construction schedules in the section of the construction organization project based on investment schedules will have a significant impact on the economic efficiency of investment projects.

Keywords: construction schedule, investments, return on investment, development of capital investments, duration of construction, efficiency of capital investments

This work solves the problem of increasing the effectiveness of educational activities by predicting student performance based on external and internal factors. To solve this problem, a model for predicting student performance was built using the Python programming language. The initial data for building the decision tree model was taken from the UCI Machine Learning Repository platform and pre-processed using the Deductor Studio Academic analytical platform. The results of the model are presented and a study was conducted to evaluate the effectiveness of predicting student performance.

Keywords: forecasting, decision tree, student performance, influence of factors, effectiveness assessment

The article synthesizes several approaches to the development of the social environment of neighborhoods and clusters, taking into account scientific developments in assessing the potential of territories in terms of building density, number of floors and capacity saturation of schools, preschool institutions and production areas. Options for implementing the strategy are outlined based on multi-product models for calculating capacity and scientific and production potential for the development of territories.

Keywords: cluster, quarter, region, potential, strategic planning, production capacity, multi-product models, building density, schematic map, optimization

Girderless ceilings have become particularly popular in the construction of civil buildings. However, it is often necessary to reconstruct them, namely, to strengthen the joint of the plate with the column. Both domestic and foreign researchers deal with the issues of punching. This scientific article is devoted to the study of the method of strengthening reinforced concrete floor slabs by adding transverse reinforcement.

Keywords: floor plate, punching, transverse reinforcement, reinforcement

The general trend in the construction of unique buildings and structures is a high degree of glazing, so that the entire shell of the object can be a translucent structure. The object of the study was translucent roofs, which solve the problem of increasing the architectural expressiveness of the object and its energy efficiency. The research methods were theoretical and empirical methods, retrospective studies of scientific and practical results. The ideas about translucent roofing structures and materials, including domed roofs, are systematized, taking into account issues of energy efficiency and the microclimate of the facility. Modern architectural, structural, materials science aspects of the development of translucent roof structures are summarized; ways to increase the energy efficiency of translucent roofing have been identified. The results of the analytical review are of interest for the development of the theory and practice of architecture of energy-efficient objects with translucent roofing.

Keywords: architecture, translucent roofing, mesh structure, shell, natural lighting, glass, dome, energy efficiency, microclimate

Prism spectral devices have a spectrum-variable dispersion and therefore a nonlinear relationship between the wavelength and the position of spectral lines on the focal surface of a spectral monochromator device, which makes it difficult to calibrate such devices in terms of wavelengths and dispersion.Most often, the well-known Hartmat formula is used for graduation. However, the accuracy of its calculation is satisfactory only in a limited spectral range, and therefore the calculation is carried out on overlapping areas no wider than 200 nm with averaging in overlapping zones. Averaging gives a calibration curve (and, accordingly, a dispersion curve) with gaps at the joints. In this paper, we consider the possibility of using a single calibration for the entire spectrum region, providing smooth, continuous calibration curves. The best result is obtained by using the Hartmann formula for the entire spectral range, after which a set of deviations of the calibration points is determined. This set is interpolated by a polynomial of an arbitrarily chosen order n using the least squares method.

Keywords: monochromator, spectrum, calibration, dispersion, Hartmann formula, interpolation, polynomial

Social and pension provision are key processes in the activities of any state, and the issues of forecasting expenses for them are among the most important in the economy. The task of evaluating the effectiveness of the pension fund has been solved by various methods, including regression analysis methods. This task is particularly difficult due to the presence of a large number of factors determining the activity of the pension fund, such as: the number of recipients of old-age pensions, the number of policyholders, self-employed policyholders, recipients of benefits, insured persons and working pensioners. As the main approach to the study, the method of implementing a model competition was applied. Those variants that violated the meaningful meaning of the variables and did not fully reflect the behavior of the modeled process were excluded from the resulting set of alternative model options. The final option was selected using the multi-criteria selection method. It is revealed that the use of relative variables is important for qualitative modeling of the studied processes. The above model shows that an increase in the ratio of the number of employers and the self-employed to the number of insured persons leads to a decrease in the cost of financing social and pension provision.The model can be effectively used for short-term forecasting of the total annual volume of financing of the pension fund department in the context of changing social and macroeconomic factors.

Keywords: pension fund, regression model, model competition, adequacy criteria, forecasting

This article analyzes data processing problems for training a neural network. The first stage of model training - feature extraction - is discussed in detail. The article discusses the method of mel-frequency cepstral coefficients. The spectrum of the voice signal was plotted. By multiplying the vectors of the signal spectrum and the window function, we found the signal energy that falls into each of the analysis windows. Next, we calculated the mel-frequency cepstral coefficients. The use of a chalk scale helps in audio analysis tasks and is used in training neural networks when working with speech. The use of mel-cepstral coefficients significantly improved the quality of recognition due to the fact that it made it possible to see the most informative coefficients. These coefficients have already been used as input to the neural network. The method with mel-frequency cepstral coefficients made it possible to reduce the input data for training, increase productivity, and improve recognition clarity.

Keywords: machine learning, data preprocessing, audio analysis, mel-cepstral coefficients, feature extraction, voice signal spectrum, Fourier transform, Hann window, discrete cosine transform, short Fourier transform

This article describes the first stage of the research work on the development of an FPGA-based camera for vehicle identification tasks, which are widely used in automated weight and size control points. Since the FPGA is an alternative to conventional processors, which features the ability to perform multiple tasks in parallel, an FPGA-equipped camera will be able to perform the functions of detecting and identifying vehicles at the same time.Thus, the camera will not only transmit the image, but also transmit the result of processing for problem-oriented control systems, decision-making and optimization of data flow processing, after which the server will only need to confirm or deny the results of the camera, which will significantly reduce the image processing time from all automated points of weight and size control.In the course of development, a simple VGA port board, a static image program for displaying it on a monitor in 640x480 resolution, and a pixel counter program were implemented. EP4CE6E22C8 is used as FPGA, the power of which is more than enough to achieve the result.

Keywords: system analysis methods, optimization, FPGA, VGA adapter, Verilog, recognition camera, board design, information processing, statistics

The article considers the information modeling of the building frame of a complex shape in the plan. The Dynamo program for Autodesk Revit is used to build the geometry. The main goal was to achieve uniform color pressure maps when blowing a building using simulation modeling in an Autodesk CFD PC. The research method is numerical (finite element method). The LIRA-CAD software package was used. The finite element method was used to select the shape of the building and adjust its design scheme to achieve reliability and efficiency. The analysis of the structural elements of the object on the effect of wind loads, taking into account the pulsation component of the wind load, is carried out in order to improve the design decisions made.

Keywords: information modeling, finite element method, building frame, node system, modal analysis, waveforms

The article discusses the existing methods for calculating the strength of a normal section in multilayer bending structures. The experience of Russian and foreign researchers was analyzed, the approaches described in domestic and foreign regulatory documents were compared, and key differences were identified. At the same time, special attention is paid to the mathematical description of the work of concrete as a material. It was concluded that further research is expedient to find the most optimal method for calculating multilayer structures.

Keywords: concrete, reinforced concrete, multilayer structures, calculation method, bending element, normal section, stresses, high-strength concrete, stress diagram, description of concrete work, bending moment, neutral axis

The choice of equipment of technological enterprises, especially when the characteristics of the equipment are close in values, remains an urgent task. In our work, to evaluate the effectiveness of programmable logic controllers (PLCs), a comprehensive criterion for evaluating efficiency is proposed, as well as a method for calculating it using numerical methods. To calculate the complex efficiency criterion, the values of the significant characteristics of the controllers selected by us are converted into points on a linear scale. To refine the calculation results, we applied one of the Newton-Cotes numerical methods, namely the trapezoid method. Next, we used the method of cubic interpolation of the obtained curves to increase the accuracy of calculations. The proposed method is simple and does not require a lot of calculations. At the same time, its application makes it possible to calculate complex PLC efficiency criteria based on characteristics relevant to a particular control process.

Keywords: programmable logic controller, characteristics, numerical methods, trapezoid method, cubic interpolation method, aggregation of characteristics, ABAK PLC, Siemens PLC, OWEN PLC

From the preservation of historical character to the introduction of environmental practices and the promotion of cultural adaptation, these methods together rethink the sustainable evolution of industrial buildings, illustrating their global prevalence and profound impact on the creation of functional, culturally resonant and visually attractive public spaces.

Keywords: renovation of an industrial building, sustainable architecture, reconstruction, energy conservation, energy efficiency, environmental friendliness, green architecture, eco-friendly design, architectural and environmental renovation