Mathematical modeling in artificial intelligence: theoretical foundations and modern applications

Bobokulova, Durdona, Бобокулова, Дурдона, Boboqulova, Durdona

Жамият ва инновациялар / Общество и инновации / Society and innovations · 2026-yil

Annotatsiya

Artificial Intelligence (AI) has become one of the most rapidly developing fields of modern science and technology, significantly influencing various sectors, including healthcare, finance, transportation, education, and industry. The effectiveness of AI systems is largely determined by the strength of their mathematical foundations. Mathematical modeling provides the theoretical framework for developing, training, optimizing, and evaluating intelligent algorithms. This study analyzes the theoretical foundations of mathematical modeling in artificial intelligence and examines its modern applications. The research focuses on the roles of linear algebra, probability theory, mathematical statistics, differential equations, and optimization methods in the development of AI algorithms. Furthermore, the mathematical principles underlying neural networks, machine learning, and deep learning models are discussed, together with their applications in healthcare, finance, transportation, and education. The findings demonstrate that mathematical modeling plays a fundamental role in improving the accuracy, stability, computational efficiency, and reliability of artificial intelligence systems. The study also highlights current challenges and future research directions in the field of mathematical modeling for artificial intelligence.

Maqola ma’lumotlari
MualliflarBobokulova, Durdona, Бобокулова, Дурдона, Boboqulova, Durdona
JurnalЖамият ва инновациялар / Общество и инновации / Society and innovations
NashriyotIn Science МЧЖ
ISSN2181-1415
Nashr sanasi2026-07-25
Jild7
Son7/S
Betlar298-308
TilIngliz
Ilmiy sohaPedagogika
DOI10.47689/2181-1415-vol7-iss7/s-pp298-308
Indeksga qo‘shilgan2026-08-26

DOI: 10.47689/2181-1415-vol7-iss7/s-pp298-308 · Maqolaning asl sahifasi

Kalit so‘zlar

искусственный интеллект, математическое моделирование, линейная алгебра, машинное обучение, глубокое обучение, нейронные сети, оптимизация, градиентный спуск, теория вероятностей, artificial intelligence, mathematical modeling, linear algebra, machine learning, deep learning, neural networks, optimization, gradient descent, probability theory, sun’iy intellekt, matematik modellashtirish, chiziqli algebra, mashinali o‘qitish, chuqur o‘qitish, neyron tarmoqlar, optimallashtirish, gradient tushish, ehtimollar nazariyasi

Ilmiy soha

Pedagogika

Iqtibos keltirish

APABobokulova, Durdona, Бобокулова, Дурдона, & Boboqulova, Durdona (2026). Mathematical modeling in artificial intelligence: theoretical foundations and modern applications. Жамият ва инновациялар / Общество и инновации / Society and innovations, 7(7/S), 298-308. https://doi.org/10.47689/2181-1415-vol7-iss7/s-pp298-308
GOST (OAK)Bobokulova, Durdona, Бобокулова, Дурдона, Boboqulova, Durdona Mathematical modeling in artificial intelligence: theoretical foundations and modern applications // Жамият ва инновациялар / Общество и инновации / Society and innovations. – 2026. – T. 7, № 7/S. – P. 298-308. – DOI: 10.47689/2181-1415-vol7-iss7/s-pp298-308.
MLABobokulova, Durdona, Бобокулова, Дурдона, and Boboqulova, Durdona. “Mathematical modeling in artificial intelligence: theoretical foundations and modern applications.” Жамият ва инновациялар / Общество и инновации / Society and innovations, 7(7/S), 298-308, 2026. https://doi.org/10.47689/2181-1415-vol7-iss7/s-pp298-308
ChicagoBobokulova, Durdona, Бобокулова, Дурдона, and Boboqulova, Durdona. “Mathematical modeling in artificial intelligence: theoretical foundations and modern applications.” Жамият ва инновациялар / Общество и инновации / Society and innovations, 7(7/S), 298-308 (2026). https://doi.org/10.47689/2181-1415-vol7-iss7/s-pp298-308
HarvardBobokulova, Durdona, Бобокулова, Дурдона, and Boboqulova, Durdona (2026) ‘Mathematical modeling in artificial intelligence: theoretical foundations and modern applications’, Жамият ва инновациялар / Общество и инновации / Society and innovations, 7(7/S), 298-308. https://doi.org/10.47689/2181-1415-vol7-iss7/s-pp298-308
BibTeX
@article{bobokulovadurdona2026,
  title = {Mathematical modeling in artificial intelligence: theoretical foundations and modern applications},
  author = {Bobokulova, Durdona and Бобокулова, Дурдона and Boboqulova, Durdona},
  journal = {Жамият ва инновациялар / Общество и инновации / Society and innovations},
  year = {2026},
  volume = {7},
  number = {7/S},
  pages = {298-308},
  doi = {10.47689/2181-1415-vol7-iss7/s-pp298-308},
  url = {https://doi.org/10.47689/2181-1415-vol7-iss7/s-pp298-308}
}

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