INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 08,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
339
APPLICATION OF MATHEMATICAL ALGORITHMS BASED ON ARTIFICIAL
INTELLIGENCE IN PRODUCTION
Jurakulova Munisa Uktam kizi
3rd year student of applied mathematics
Jizzakh Branch of the Mirzo Ulugbek National University of Uzbekistan
Abstract:
This article examines the theoretical and practical aspects of the integration of
artificial intelligence (AI) and mathematical modeling for the production sector. Also, in the
context of modern Industry 4.0, the processes of machine learning and predicting failures using
mathematical algorithms based on large volumes of IoT data in real time, virtual simulation and
optimization of processes using digital twins technology are analyzed.
Keywords:
Mathematical modeling, artificial intelligence, mathematical algorithms, digital
twins technology, neural networks, Predictive Maintenance methodology
Аннотация:
В данной статье рассматриваются теоретические и практические аспекты
интеграции искусственного интеллекта (ИИ) и математического моделирования для
производственной сферы. Также в контексте современной Индустрии 4.0
проанализированы процессы машинного обучения и прогнозирования сбоев с
использованием математических алгоритмов на основе больших объемов данных IoT в
режиме реального времени, виртуальное моделирование и оптимизация процессов с
использованием технологии цифровых близнецов.
Ключевые слова:
Математическое моделирование, искусственный интеллект,
математические алгоритмы, технология цифровых близнецов, нейронные сети,
методология Прогностического обслуживания
Annotatsiya:
Mazkur maqolada sun’iy intellekt (AI) va matematik modellashtirish
integratsiyasining ishlab chiqarish sohasi uchun nazariy va amaliy jihatlari o‘rganib chiqildi.
Shuningdek, zamonaviy sanoat 4.0 sharoitida real‑vaqt rejimidagi katta hajmdagi IoT
ma’lumotlari asosida mashina o‘rganish va matematik algoritmlar yordamida nosozliklarni
oldindan bashorat qilish, digital twins texnologiyasi orqali jarayonlarni virtual simulyatsiya
qilish va optimallashtirish jarayonlari tahlil qilinadi.
Kalit so‘zlar:
Matematik modellashtirish, sun’iy intellekt, matematik algoritmlar, digital twins
texnologiyasi, neyron tarmoqlar, Predictive Maintenance metodologiyasi
INTRODUCTION
In recent years, as a result of the rapid development of science and technology, mathematical
modeling and artificial intelligence (AI) have become an integral part of our daily lives.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 08,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
340
Mathematical modeling is one of the important scientific approaches used to understand,
analyze, and predict complex processes in the real world. Artificial intelligence allows the
creation of intelligent systems capable of making decisions similar to human thinking. Today,
the mutual integration of these two areas serves to increase efficiency in various fields and the
development of new innovative approaches. Moreover, in the era of modern industry 4.0,
production processes are becoming increasingly complex, and to ensure their effectiveness, a
huge amount of real-time data is being created - IoT sensors, monitoring systems, dynamic
changes in production parameters - for analysis and management. Traditional engineering and
economic theories cannot adequately process this complex flow of information. Therefore,
approaches prepared for mathematical algorithms based on artificial intelligence are emerging
as an important tool for optimizing production processes, predicting failures, and making real-
time decisions. [1]
At present, with the help of mathematical algorithms and modeling, it is possible to deeply
study existing problems in such areas as natural sciences, economics, engineering, ecology,
biomedical science, and determine the dynamics of their development. For example,
mathematical models are widely used in economics to predict market trends, in ecology to
monitor climate change, or in medicine to analyze the spread of diseases. Artificial intelligence,
in turn, creates the possibility of processing, classifying, and forecasting large amounts of data.
Thanks to AI technologies, such as machine learning, in-depth learning, and neural networks, it
is possible to automatically analyze medical images, develop automated control systems in
industrial robotics, and create intelligent navigation systems in the transport sector.
Currently, mathematical algorithms based on artificial intelligence are widely used in the
following areas: Finance (FinTech), Healthcare (Healthcare & Pharma), Manufacturing
(Manufacturing & Advanced Manufacturing), Energy and Alternative Energy (Energy),
Logistics and Transport (Transportation & Logistics), Agriculture (Agriculture). [2]
In particular, in the financial sector, services such as fraud detection, risk management,
algorithmic trading, chatbots, and robo-advisors have been automated using AI. In the field of
healthcare, AI is used in diagnostics, disease prediction, personalized medicine, and particle
models. In these areas, physiological and drug testing models are built using statistical models,
ML regression, genetic algorithms, and GAN/ANN networks. In agriculture, AI models for
precision farming, drone imagery analysis, disease prediction, and livestock monitoring are
widely used. Regression, time-series analysis, classification, and clustering algorithms play a
key role in these.
MAIN PART
Indeed, today the integration of artificial intelligence (AI) and mathematical modeling - that is,
the transformation of industrial processes into a digital model through machine learning
algorithms, optimization methods, physics-informed neural networks (PINN) - significantly
increases production efficiency. For example, the predictive maintenance approach identifies
equipment malfunctions by analyzing sensor data and predicting maintenance times, while
digital twins technology allows simulating and optimizing processes by creating a virtual copy
of the real network [3].
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 08,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
341
If inaccurate or low-quality data is used in the modeling or machine learning process, the results
may also be inaccurate. This can affect the results of economic forecasts, medical diagnostics,
and environmental analyses. Efficiency of computational resources and algorithms. Artificial
intelligence and mathematical modeling processes require large computing power. Especially
for the operation of deep learning models, there is a need for high-level GPU or quantum
computer technologies. This creates financial and technological constraints for small and
medium research centers and enterprises. Ethical and Legal Issues The use of artificial
intelligence creates problems such as the confidentiality of personal data, the adoption of
incorrect decisions by AI systems, and the impact on jobs. Especially in the fields of medicine
and safety, incorrect decisions can have a serious impact on human life. Therefore, it is
important to clearly define ethical and legal norms in the development of artificial intelligence.
A mathematical algorithm is a strictly defined, precise, and repetitive sequence of operations
for solving a specific problem. Basic mathematical algorithms and their applications: Genetic
algorithms (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO) [4]
These metaheuristic optimization approaches are used to solve complex combinatorial problems
such as production scheduling, resource allocation, and energy consumption reduction. Their
application leads to scalability, efficient planning, and time reduction.
Reinforcement learning (RL) - for the development of automatic control systems based on real-
time feedback, AI agents make decisions using RL and optimize the system. [5]
In Predictive Maintenance, real-time data is collected through Sed or IoT sensors, then the
equipment's failure propensity is predicted using ML models (for example, optimized with
Random Forest, XGBoost, Deep Learning, SVM GA). As a result, downtime during production
time is reduced by 20-50%, and costs are significantly reduced.
DISCUSSION AND RESULTS
The Predictive Maintenance methodology provides effective results in enterprises. Based on the
conducted research, unexpected technical downtime is reduced by 30-50%, service costs are
reduced by 20-40%, and the equipment's service life is extended by 20-30%. [6]
There is a significant shortage of qualified specialists in the necessary AI/analysis at enterprises
and resistance of employees to new technologies. There is a need for retraining and the
formation of an innovative culture so that systems are ready for the necessary loading.
AI systems increase risks associated with cybersecurity threats, data privacy, and legal norms.
AI-based mathematical algorithms have great potential in optimizing investments, increasing
operational efficiency, and ensuring the stability of production systems
.
Real examples and
empirical results provide real economic benefits in important functions such as technical
condition forecasting, quality control, and planning based on AI. At the same time, when
implementing the technology, serious attention should be paid to financial, personnel, data, and
regulatory issues. Through proper planning and sustainable integration, AI-optimization
approaches ensure long-term and sustainable production.
CONCLUSION
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 08,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
342
In conclusion, mathematical algorithms based on artificial intelligence (AI), in particular
predictive maintenance, optimization, and virtual simulation tools, raise production processes to
a new level. AI is used to predict malfunctions and provide scheduled maintenance. This
approach reduces unplanned downtime by 20-50%. As a result, operational efficiency and
production quality increase, and product delivery prospects improve.
Various scenarios are tested using mathematical algorithms - GA, PSO, ACO, RL, and PINN -
and the most optimal option is selected. This approach allows one to act confidently when
scientifically substantiating the long-term development strategy of the enterprise. Indeed,
mathematical algorithms based on artificial intelligence are becoming a central tool for
predicting malfunctions in the production sphere, saving costs, efficient use of resources,
quality control, and creating a stable production system. They create a solid scientific and
practical basis for resource optimization, automation of production processes, and strategic
development of enterprise management.
REFERENCES:
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https://www.isixsigma.com/artificial-intelligence/the-industries-that-will-benefit-the-most-
3. Justin Ogala, Ohoriemu Blessing Okeoghene “Integrating Artificial Intelligence and
Mathematical Models for Predictive Maintenance in Industrial Systems” (2024)
4. Ucar, A., Karakose, M., & Kırımça, N. (2024). Artificial Intelligence for Predictive
Maintenance Applications: Key Components, Trustworthiness, and Future Trends. Applied
Sciences
5. Windmann, A., Wittenberg, P., Schieseck, M., Niggemann, O. (2024). Artificial Intelligence
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