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June 5, 2026
Neural Network Maps as a Method for Constructing Mathematical Models
Scientists from HSE University–Nizhny Novgorod and the Institute of Physics Belgrade, Serbia, are jointly exploring the application of machine learning techniques and neural networks to the study of nonlinear dynamics. Natalya Stankevich, Leading Research Fellow at the Laboratory of Topological Methods in Dynamics of the Faculty of Informatics, Mathematics, and Computer Science at HSE University–Nizhny Novgorod, spoke to the HSE News Service about this international project.
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Researchers from the AI and Digital Science Institute at the HSE Faculty of Computer Science have developed a new compression method for large language models such as GPT and LLaMA that reduces their size by 25–36% without additional training or significant loss of accuracy. This is the first approach to use mathematical transformations—specifically, rotations of model weights—to make models more amenable to compression with structured matrices. The study results have been published in ACL Findings 2025. The code is available on GitHub.

 

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Атмосферные фронты и их 3D-визуализация

Гл. 5. С. 25–31.
Беззубцев А. С., Быков Ф. Л., Gordin V. A.

Algorithms for three-dimensional visualization of atmospheric front surfaces have been developed. Previously, the technology of visualization of intersections of atmospheric fronts with isobaric levels was implemented. These are curves that show the intensity and type of the atmospheric front in color. At this stage, it was necessary a) to find out which curves at different levels correspond to the same two-dimensional surface in three-dimensional space; b) to build approximations of these surfaces. A significant problem for constructing the algorithm: the curves are not submitted analytically, but by pixels on a rectangle. Curves can branch. The developed algorithms use spline-approximation of curves and approximation by Bezier surfaces. The resulting surfaces can be "viewed" on the screen at different spatial scales and at different angles, i.e. simulated "exploration" of the surfaces of atmospheric  fronts. The initial information for this technology is the prognostic output of the COSMO-ru scheme. Therefore, the user will be able to monitor the dynamics of the surfaces of atmospheric fronts and their intensity to make operational decisions to optimize the flight trajectory.

Language: Russian
Full text
Keywords: траектория полетаAtmospheric front intensitybaric levelstwo-dimensional surfacesbranching curvesspline approximationПоверхность Безьеflight trajectoryИнтенсивность атмосферного фронтабарические уровнидвумерные поверхностиветвление кривыхсплайн-аппроксимацияBezier surface
Publication based on the results of:
Математические модели. Дифференциальные уравнения и большие массивы информации. Аналитические и вычислительные методы. Практические приложения (2018)

In book

Современные проблемы математического моделирования: сборник трудов XVIII Всероссийской конференции-школы молодых исследователей (пос. Абрау-Дюрсо, 16–20 сентября 2019 г.)
Ростов н/Д: Издательство ЮФУ, 2019.
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