Bulletin of V.N. Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems»

Hybrid Neural Network Model Based on CNN+Transformer for Predicting the Spectral Properties of Multilayer Structures

Yurii Bilak — 2025-12-22

Relevance. Predicting the spectral characteristics of multilayer materials is a key task in photonics, optoelectronics, and materials science, as the accuracy of modeling directly affects the efficiency of technological processes and the performance of functional coatings. Classical numerical methods ensure reliable calculations but become computationally demanding when many parameter variations are required. This motivates the development of hybrid architectures that combine physical modeling with the capabilities of modern neural networks.

Goal. The aim of this work is to develop and investigate a hybrid neural network model based on a CNN+Transformer architecture for predicting the spectral characteristics of multilayer structures, and to evaluate its effectiveness in comparison with classical and alternative neural network methods.

Research methods. Training data were generated using the TMM in the spectral range of 300–800 nm. PCA was applied to optimize spectral representation, reducing the number of spectral points while preserving 98% of the data variance. The neural model integrates convolutional layers for extracting local interference-related features and a transformer block for capturing global dependencies. The training process employed a loss function that combines prediction accuracy with regularization, while model validation was performed on an independent test dataset.

The results. The proposed model demonstrated high predictive accuracy, achieving a determination coefficient of R² = 0.99 and a mean squared error below 4%. A comparison with the CNN+LSTM architecture revealed the advantage of the transformer-based model, which more effectively captures long-range spectral correlations and provides faster inference. The model showed strong agreement with TMM-generated reference data and maintained robustness to noise variations in experimental spectra.

Conclusions. The developed hybrid CNN+Transformer model proved to be an effective tool for predicting the spectral characteristics of multilayer structures. Combining physical modeling with deep neural networks ensures high accuracy, computational speed, and generalization capability. The results highlight the promise of this architecture for fast optical analysis and thin-film structure optimization. Future work may include expanding the training dataset, accounting for nonlinear optical effects, and integrating the model into automated design systems for optical materials.

Digital Twin Development for the Heat Transfer Process under Conceptual Uncertainty

Igor Golinko — 2025-12-22

Relevance. Industrial development is characterized by the active introduction of cyber-physical systems, a key element of which is digital twins. Digital twins make it possible to improve the efficiency of technological process management, ensure the prediction of equipment operating modes, optimize energy consumption, and reduce operating costs. Water heaters are an important component of heat generation and consumption systems in industrial facilities, which necessitates the creation of adequate models capable of accurately reflecting real heat exchange processes. However, analytical models of such equipment often contain uncertain parameters, which reduces the accuracy of modeling and complicates their practical application without additional identification.

Purpose of the publication is to develop a water heater digital twin based on an analytical model adapted to real heat exchange conditions by identifying uncertain parameters. The analytical model is considered as a basic example that can be generalized for different types of heat exchange equipment.

Methods. The work uses analytical modeling of thermal processes and passive identification methods of mathematical model parameters. The dynamic model is adapted by minimizing the quadratic quality criterion, which characterizes the deviation of the state space variables of the mathematical model from the experimental data of the real heat transfer process. Numerical methods are used for passive identification.

Results. An analysis of the analytical mathematical model of a water heater was carried out and four uncertain parameters were identified that need to be refined to ensure the adequacy of the model. These parameters include material flows rates and heat transfer coefficients that determine the intensity of the heat flow through the heat exchange surface of the device. Based on numerical modeling, it is shown that the task of identifying uncertain coefficients is single-extreme in nature, which ensures the stability of optimization results and the possibility of applying standard numerical methods. The results of numerical modeling confirmed the effectiveness of the proposed approach to adapting the analytical model and developing a digital twin of a water heater.

Conclusions. The proposed approach to the digital twin development of a water heater provides an adequate reproduction of the real heat exchange process and can be used as part of industrial enterprises cyber-physical systems. The considered identification method can be easily extended to other types of heat exchange equipment used in heat generation and consumption systems.

Method for generating source code description using an artificial intelligence model

Albina Kostiuchenko — 2025-12-22

Relevance. The topic is relevant, since currently there are many large projects that are being developed over a long period of time and require support and understanding of the code without explanations. The rapid development of technologies and the need to constantly develop new features and support existing ones require constant updating of documentation. Writing good documentation is a valuable skill that requires experience, concentration and understanding of the project structure. As a result, a large number of developers consider the process of writing documentation difficult and think that the time spent on it could be used more productively. That is why there is a demand for services that help automate this process.

Goal. The purpose of this work is to increase the efficiency of automated generation of software documentation. As part of this task, the necessary theoretical material was worked out, existing solutions to this problem were studied, and our own new method of generating a description of the program code was developed and implemented, which more accurately determined the purpose of code fragments, clearly understood the structure and dependencies between its components.

Research methods. The study is based on literature analysis, statistical methods, as well as machine learning and data mining methods. In particular, the methods of syntactic code analysis and construction of an abstract syntax tree (AST), the method of forming a training corpus, methods of training and retraining of transformer and graph models were used. To assess the advantages of the retrained model, the method of comparative modeling and automated text quality assessment (in this case, BERTScore) was used.

The results. Retraining the T5 model on a specialized dataset with commented code in combination with lexical analysis allowed to increase the quality of generation by approximately 4% in terms of the F1 metric compared to the base model. This indicates that adapting the model to a specific domain task is effective and can significantly improve the result.

Conclusions. Based on the collected data, an own approach was proposed to improve the quality of code description generation using the retrained T5 model and the created GNN model with further implementation, which is the result of the research. The proposed system combines the best practices of syntactic analysis, graph modeling, and transformer generation, providing a practically applicable solution for automatic documentation creation. It can be argued that the combination of "seq2seq" models, tokenization and adaptation methods of large transformers, as well as code analysis via GNN and structural AST representations provides a comprehensive approach to automating work with code, allowing you to combine local and global contexts, quickly adapt the model to specific tasks, and effectively generate meaningful comments and documentation. Such an integrated approach has the potential for further development of artificial intelligence systems in the field of automatic code analysis, increasing developer productivity, and ensuring software quality. The research results can be applied in practice for fast and effective creation of documentation for developed software and large projects in the Python language.

Bending analysis of multiply-connected anisotropic plates with elastic inclusions

Andrii Koshkin — 2025-12-22

Relevance. Determining the stress-strain state of thin anisotropic plates with foreign elastic inclusions under transverse bending is an important engineering problem. However, the general case of a plate with multiple, arbitrarily arranged inclusions has lacked an effective numerical or analytical solution due to significant mathematical and computational difficulties.

Objective. The purpose of this work is to develop a new approximate method for determining the stress state of a thin anisotropic plate containing a group of arbitrarily located elliptical or linear elastic inclusions.

Methods. The method is based on the application of S. G. Lekhnitskii's complex potentials. The problem is reduced to determining functions of generalized complex variables for the plate-matrix and the inclusions. These potentials are represented by corresponding Laurent series and Faber polynomials. The generalized least squares method (GLSM) is used to satisfy the contact boundary conditions on the inclusion contours. This reduces the problem to an overdetermined system of linear algebraic equations, which is solved using singular value decomposition (SVD).

Results. The developed method was validated by comparison with the known exact analytical solution for a plate with a single elliptical inclusion, showing perfect agreement. Numerical studies were conducted to analyze the influence of the relative stiffness of the inclusions, the distances between them, and their geometric characteristics on the bending moment values. It was established that the interaction between inclusions is significant and leads to a substantial increase in moments at small distances. Isotropic plates are considered as a special case of anisotropic ones.

Conclusions. It was established for the first time that for linear elastic inclusions, moment singularities, described by moment intensity factors (MIFs), occur only in cases of sufficiently stiff or sufficiently flexible inclusions.

Analysis of Modern Neural Network Methods for Visual Information Processing in High-Speed UAV Navigation Systems

Antonii Lupandin — 2025-12-22

Relevance. The rapid evolution of Unmanned Aerial Vehicles (UAVs) from remotely piloted systems to fully autonomous high-speed aerial robots has intensified the demand for advanced onboard perception and navigation methods. This need is particularly acute in scenarios where computational latency, sensor noise, and environmental complexity undermine the reliability of classical computer-vision pipelines. Despite recent progress in deep learning, the existing approaches to visual information processing—especially CNN-based detectors, Transformer-based semantic models, and learning-enhanced SLAM modules—remain fragmented and insufficiently adapted to the strict Size, Weight and Power (SWaP) constraints of embedded platforms such as the NVIDIA Jetson series. This motivates a comprehensive analysis of modern neural architectures suitable for real-time, high-velocity UAV operations.

Purpose. The purpose of this study is to analyze state-of-the-art neural network methods for secondary visual processing in UAV navigation systems, compare the applicability of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), evaluate their integration into SLAM pipelines, and determine the requirements for hybrid architectures capable of supporting fully autonomous, high-speed flight.

Methods. The research employs a comparative analysis of recent deep-learning approaches, including CNN-based detectors (YOLO family), Transformer-based visual models, deep-learning–enhanced SLAM components, and Deep Reinforcement Learning (DRL) control policies. Evaluation criteria include latency, semantic robustness, dynamic-scene handling, edge-hardware compatibility, quantization performance, pruning potential, and TensorRT optimization efficiency on NVIDIA Jetson devices.

Results. The study establishes that CNNs provide superior real-time performance and remain indispensable for high-frequency reflexive perception, while Vision Transformers offer stronger global context reasoning and robustness to occlusion but suffer from significant computational overhead on embedded GPUs. Deep-learning-based SLAM methods improve feature stability and dynamic-object rejection but require careful integration to maintain real-time constraints. Hardware analysis reveals that quantization, pruning, and TensorRT acceleration are critical for deploying deep models on Jetson-class platforms, although ViTs exhibit limited INT8 quantization tolerance. Based on these findings, the work formulates a conceptual hybrid architecture that combines CNN-driven reflexive processing with Transformer-driven cognitive reasoning.

Conclusions. The results confirm the necessity of developing hybrid neuro-architectures that integrate the speed and hardware efficiency of CNNs with the semantic depth of Transformer-based models. Such architectures represent a promising pathway toward reliable, fully autonomous high-speed UAV navigation. The proposed design principles emphasize hierarchical control, asynchronous perception loops, and hardware-aware optimization as key enablers for next-generation aerial robotic systems.

Reflective memory architecture for adaptive planning in hierarchical LLM agents in virtual environments

Ihor Omelchenko — 2025-12-22

Relevance: Large language models (LLMs) can be used as one of the components of autonomous agents that solve sequential decision-making tasks. To improve agent performance, it is necessary to store the history of previous observations and actions, which leads to filling the LLM context window, increasing computational costs, prolonging planning time, and raising memory requirements. A possible approach to addressing this problem is the application of observation reflection methods using LLMs.

Goal: To study the impact of memory reflection methods for autonomous agents based on LLMs. To compare these methods with simpler memory organization approaches.

Research methods: Computational experiments and comparative analysis. Memory organization methods: full episode history, reflection, and reflection with a structured set of memories. The agent performance metrics: task success rate, cumulative reward per episode, and the number of steps required to complete the task.

Results: A memory summarization method based on reflection is proposed for a hierarchical LLM-based agent. The Minigrid ColoredDoorKey environment is used for agent training. Agent code is developed, including components for training the agent in the environment. Computational experiments are conducted to train and evaluate the agent with different memory mechanisms. The performance of different memory mechanisms is evaluated using the following metrics: task completion accuracy, cumulative reward, and the number of steps until episode termination. An analysis and comparison of the results of applying different memory mechanisms to the agent’s action planning task in the ColoredDoorKey environment are performed.

Conclusions: The study demonstrates that the use of reflection with a structured set of memories is appropriate for action planning tasks in autonomous agents based on LLMs. The reflection method enables the agent to generalize experience, identify effective rules within large volumes of data with sparse reward signals, and achieve a level of performance comparable to that of a human expert.

Method of power supply optimization for iot climate monitoring system based on adaptive algorithms

Illia Stetsiurenko — 2025-12-22

Relevance. The rapid growth of the Internet of Things (IoT) has led to the massive deployment of autonomous sensor nodes in remote locations, such as precision agriculture and environmental monitoring. These devices rely heavily on battery power, making energy efficiency a critical factor for system viability and maintenance costs. Traditional static data transmission schedules are inefficient, wasting energy during stable conditions or missing critical data during rapid environmental changes. Therefore, developing adaptive energy management strategies is highly relevant.

Goal. The study aims to develop a method for optimizing the power supply of an IoT climate monitoring system based on adaptive algorithms and to conduct a comparative analysis of the energy efficiency of different communication architectures (Wi-Fi, BLE, LoRaWAN) to identify optimal solutions for various operational scenarios.

Research methods. An experimental-analytical approach was used. The hardware platform was built on the ESP32 microcontroller and BME680 sensor. A finite state machine model was proposed to manage device states, implemented in two paradigms: local adaptation (decision-making on the device) and cloud adaptation (control via AWS Lambda). A series of field measurements were conducted for five communication protocols: HTTP, MQTT, CoAP (over Wi-Fi), BLE, and LoRaWAN, testing four evolutionary software versions from basic to fully adaptive.

Results. The experiments confirmed the effectiveness of the proposed approach. For Wi-Fi networks, switching to the CoAP protocol with an adaptive algorithm reduced the average current consumption from 60.46 mA (baseline) to 12.47 mA, achieving savings of about 79%. For the LoRaWAN architecture, a reduction from 96.78 mA to 12.63 mA (87% savings) was achieved. It was found that cloud-based adaptation is less effective for "heavy" protocols like MQTT due to latency.

Conclusions. The integration of adaptive algorithms that dynamically control the sleep interval allows for a reduction in energy consumption by 70-87% compared to baseline modes. For systems with Wi-Fi infrastructure, the CoAP protocol is the most energy-efficient. For tasks requiring maximum autonomy and range, LoRaWAN with a local adaptive algorithm is the optimal choice.

Adaptive context management in RAG systems for personalized AI assistants

Andrii Suprun — 2025-12-22

Relevance. The development of artificial intelligence systems based on large language models (LLMs) highlights the problem of effective dialogue context management, as conventional history storage mechanisms often lead to context overload and a reduction in response generation quality. This problem is particularly acute in Retrieval-Augmented Generation (RAG) systems, where dialogue memory is combined with dynamic retrieval of external knowledge, creating an additional burden on the model's limited context window. Existing approaches to context management do not provide an adaptive mechanism for dialogue context formation that accounts for individual user characteristics and domain specificity. Goal. Development and testing of an Adaptive Context Management System (ACMS) for personalized RAG assistants, which combines a sliding window of recent messages, compressed summaries of long-term history, and personalized knowledge retrieval from the database. Research methods. A microservice architecture has been developed, including an AI Orchestrator for coordinating the RAG process, a vector search service based on PostgreSQL with pgvector extension, and a central ACMS component for context management. The proposed approach synthesizes three strategies: sliding window to preserve the last N messages, LLM-based compression of old history fragments into thematic summaries, and a personalization layer for weighting relevance based on user vector profiles. Final context formation is performed through adaptive mixing of dialogue history and relevant knowledge from the database, taking into account individual user profiles. Results. The experimental evaluation demonstrated significant advantages of the adaptive system compared to the baseline approach. In pairwise comparisons, the adaptive system proved superior in 62% of cases (Answer Win-Rate = 0.62). The key factor for improvements was the personalization layer, which reduces repetitions and off-topic content from dialogue history, provides targeted amplification of relevant documents, and enables flexible regulation of the balance between history and knowledge. Conclusions. The developed adaptive context management system provides effective dialogue context management in RAG systems for personalized AI assistants. The integration of compression strategies, adaptive window, and user personalization enabled a 14% increase in response relevance and a 22% optimization of context volume. Experimental validation confirmed the practical feasibility of the proposed approach across different subject domains, as well as system scalability when working with large volumes of historical data.

Analysis of the effectiveness of the Resemblyzer library for short-command voice authentication

Mykhaylo Trusov — 2025-12-22

Relevance. Voice interaction is widely used in Internet of Things systems and autonomous embedded devices. However, its practical deployment is constrained by security and privacy requirements as well as the limited computational resources of edge platforms. This creates a demand for fully local voice authentication solutions capable of operating without reliance on cloud services. Goal. The objective of this study is to evaluate the capabilities of the open-source Python library Resemblyzer for implementing autonomous user voice authentication based on short voice commands under conditions of no access to cloud computing and limited hardware resources. Research methods. The study was conducted using several audio datasets with varying duration, quality, and file size. Voice embeddings generated by the Resemblyzer library were used for feature representation. Quantitative similarity assessment between recordings was performed using the cosine similarity metric in scenarios involving comparisons of recordings from the same speaker and from different speakers.

Results. The results demonstrate that reliable voice authentication is achieved for audio recordings with a duration of at least 2.63 seconds and a file size of no less than 495 kB. Short fragments with durations of 1-1.5 seconds were found to be insufficiently informative for stable speaker discrimination, particularly when compared against a high-quality reference recording. A clear dependence of authentication performance on the amount of acoustic information contained in the voice signal was identified.

Conclusions. The obtained results confirm the aplicability of Resemblyzer for the development of fully autonomous real-time voice biometric authentication systems. Practical requirements for the minimum duration and informational richness of voice commands are formulated, which may be interpreted as technical constraints on the entropy of voice passwords in secure IoT applications.

The use of machine learning methods in modern mathematical oncology

Ivan Tiurdo — 2025-12-22

The purpose of the study is to analyze modern approaches to assessing the efficacy and safety of anti-cancer drugs using machine learning methods, as well as to determine the prospects for their use in modern mathematical oncology, in oncological research that widely uses mathematical modelling and simulation.

As a result of the study, a literature review was conducted on the use of machine learning in oncology. An analysis of the use of the main machine learning methods, such as Supervised Learning (SL), Unsupervised Learning (UL), and Reinforcement Learning (RL) in modern oncology was performed. Examples of the use of various machine learning algorithms in research related to anti-cancer therapy and oncology in general are given. The advantages and disadvantages of the used machine learning algorithms are analyzed depending on the tasks to be solved.

Conclusions: Machine learning methods are already widely used in medical research in the field of oncology. They have been successfully applied to solve many issues and showed good results, but there are still many areas in oncology where the use of machine learning methods can make a significant contribution to improving medical research and medical care in the treatment of cancer. For example, the use of algorithms based on reinforcement learning in precision medicine looks very promising, as its methods play a significant role in the personalized treatment of cancer.

An expert system for evaluating language patterns using nonparametric statistics

Tetiana Shabelnyk — 2025-12-22

Abstract. The paper focuses on the research of language regularities by methods of non-parametric statistics. The emphasis is placed on how to resolve the common problems regarding the use of non-parametric statistical techniques, in particular the one of semantic marking of sentences in linguistics.

The aim of the scientific research is defined as the development of an expert system for evaluating language regularities using non-parametric statistical methods for any language.

Research methods. Methods of non-parametric statistics, IDEF4 notation, the programming language C #.

The research offers a specialized expert system that uses the C Programming Language to provide automatic questioning of the native speakers with further analysis of the lexical meaning of word combinations and phrases implemented as a Desktop Program for Windows. The program considers the possibility of taking into account of how to reveal the correspondence of phrases from dictionary files that have different expert assessments.