CHEGARAVIY MASALALARNI YECHISH UCHUN SUN’IY INTELLEKT ELEMENTLARI ASOSIDAGI GIBRID INTEGRATSIYA MODELI

Nodirbek Aliyev

Авторы

Nodirbek Aliyev Автор https://orcid.org/0009-0006-2038-5755

Ключевые слова:

chegaraviy masalalar, sun’iy intellekt, gibrid integratsiya, Physics-Informed Neural Network, differensial tenglama, integrallash, neyron tarmoq, optimallashtirish, hisoblash murakkabligi, yaqinlashuv, nolinear model, dasturiy ta’minot, parallel hisoblash, Python, TensorFlow.

Аннотация

Mazkur maqolada chegaraviy masalalarni yechish uchun sun’iy intellekt elementlariga asoslangan gibrid integratsiya modeli ishlab chiqilgan. An’anaviy sonli usullar (Finite Element, Finite Difference, Spectral Methods) murakkab nolinear va yuqori o‘lchamli chegaraviy masalalarni yechishda ko‘p vaqt va katta hisoblash resurslarini talab etadi. Shu sababli, maqolada fizik qonunlarga asoslangan neyron tarmoqlar — Physics-Informed Neural Networks (PINN) konsepsiyasi asosida yangi gibrid model taklif qilinadi. Ushbu model differensial tenglamalarning chegaraviy shartlarini integratsiyalashda an’anaviy matematik algoritmlar va sun’iy intellektning o‘z-o‘zidan o‘rganish qobiliyatini birlashtiradi. Tadqiqotda hisoblash murakkabligi, xatolik darajasi va yaqinlashuv tezligi ko‘rsatkichlari tahlil qilinib, ular O‘zbekiston sharoitida ilmiy-texnik hisoblash dasturlarini avtomatlashtirish imkonini beradi. Natijalar gibrid AI-integratsiya modelining differensial masalalarni tez, aniq va barqaror yechishda samarali ekanligini ko‘rsatadi. Modelning dasturiy ta’minoti Python asosidagi TensorFlow va NumPy kutubxonalarida sinovdan o‘tkazilgan.

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