• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Решение дифференциальных уравнений с помощью языковых моделей из коробки: потенциал небольших LLM в математике
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
July 24, 2026
'Physics Is What the World Is Literally Built On'
Physicist Nina Dzhanayeva, recipient of a Vladimir Potanin Foundation scholarship, focuses her research on nanophotonics. In this interview for the HSE Young Scientists project, she discusses nanowells, scientific intuition, and how physics can help in making frangipane cream puffs.
July 20, 2026
Scientists Create Open Dataset for Studying Concentration
A team of Russian researchers, including scientists from HSE University–St Petersburg, has developed the first open multimodal dataset containing recordings of brain activity, heart function, and video observations to help researchers understand what happens in the human brain during deep concentration. In the future, the dataset could accelerate the development of neural interfaces, rehabilitation technologies, and AI systems. The article has been published in Scientific Data.
July 20, 2026
‘Science Is Universal-It Knows No Borders
Fuad Aleskerov, Tenured Professor and Director of the International Centre of Decision Choice and Analysis at HSE University, together with his colleagues, has developed methods of network analysis in bibliometrics that have made it possible to identify patterns in the appearance and citation of publications in academic journals, as well as their influence on each other. When one or a number of studies are frequently cited by a wide range of journals, this is an indicator that the research is of high quality. By contrast, extensive cross-citation within a limited group of journals increases the likelihood of identifying a network of predatory publications.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Решение дифференциальных уравнений с помощью языковых моделей из коробки: потенциал небольших LLM в математике

Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2025. Т. 527. С. 311–319.
Koltsov S., Ignatenko V., Surkov A., Захаров В. О.
Research target: Computer Science Mathematics
Language: Russian
Full text
DOI
Text on another site
Keywords: дифференциальные уравнениямалые языковые моделиQwen2.5-1.5bOpen-Reasoner-Zero-1.5bDeepSeek-R1-Distill-Qwen-1.5b
Similar publications
Квадратичный закон взаимности и его обобщения
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Three Algorithms for Merging Hierarchical Navigable Small World Graphs
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Профессиональная верификация: Руководство по продвинутой функциональной верификации
Уилкокс П., Romanov A., М.: ДМК Пресс, 2025.
Книга, которую вы держите в руках, продолжает серию «Книжная полка истового инженера», которая издается при поддержке компании YADRO. Данная книга представляет собой учебник по теоретическим основам продвинутой функциональной верификации и содержит лучшие практики, используемые в настоящее время. В ней подробно описана унифицированная методология верификации (UVM) и раскрыты такие темы, как функциональный виртуальный прототип, функциональное покрытие, утверждения, формальная верификация, тестбенчи, косимуляция, эмуляция, аппаратное ...
Added: July 30, 2026
EEG evidence for reproducible neural states during Buddhist Highest Yoga Tantra meditation
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Произведения Масси и соотношения в когомологиях алгебр Стинрода
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2. As part of a demonstration ...
Added: July 28, 2026
Three-dimensional magnetization textures as quaternionic functions
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications. Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Machine Learning-based Adaptive Reconstruction of Video Stream Fragments Taking into Account Scene Dynamics. Proceedings of the Institute for System Programming of the RAS
Думкин Н. А., Alexandrov D., Прозорский М. А., Труды Института системного программирования РАН 2026 Т. 38 № 1 С. 255–274
A theoretically sound approach to adaptive client-side video fragment restoration is proposed using machine learning and scene analysis methods. The method includes a formal problem statement, a finite-state machine model for decision making, a restoration cost function, and a new stage in video preparation: scene dynamics assessment followed by recording a feature in an HLS playlist. This feature ...
Added: July 27, 2026
Nonlinear Neumann eigenvalues in outward cuspidal domains with weighted measure
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
On the (p,q)-Eigenvalues of the No-Flux p-Laplacian
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
Automated Reasoning: 13th International Joint Conference, IJCAR 2026, Lisbon, Portugal, July 26–29, 2026, Proceedings, Part II. (LNCS, volume 16689)
Cham: Springer, 2026.
This open access set, LNAI 16688-16689, constitutes the proceedings of the 13th International Joint Conference, IJCAR 2026, held in Lisbon, Portugal, during July 26–29, 2026. The 41 full research papers and 8 short papers included in these two volumes were carefully reviewed and selected from 112 submissions. The papers cover the following topical sections: Part I: Theorem ...
Added: July 26, 2026
Local Fault-Tolerant Routing in 3D Mesh NoCs using Single-Hop Rollback
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Библиометрия фольклора: русские пословицы в научных журналах
Pislyakov V., Вестник Томского государственного университета. Филология 2026 № 101 С. 175–192
This article examines the use of proverbs in academic texts—specifically, articles published in Russian research journals. For the experiment, ten proverbs were selected as the intersection of two fundamentally different paremiological surveys aimed at compiling lists of popular or common Russian proverbs. One of these surveys was conducted by the classic of paremiology, G.L. Permyakov, ...
Added: July 22, 2026
SIGIR '26: Proceedings of the 49th International ACM SIGIR Conference on Research and Development in Information Retrieval
Association for Computing Machinery (ACM), 2026.
Wominjeka, and welcome to the 49th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR 2026), held in Melbourne | Naarm, Australia, from 20–24 July 2026. SIGIR 2026 takes place on the unceded lands of the Woi Wurrung and Boon Wurrung language groups of the eastern Kulin nation, and we pay our ...
Added: July 22, 2026
Long-range machine-learning potentials with environment-dependent charges enable predicting LO-TO splitting and dielectric constants
Korogod D., Shapeev A., Ivan S. Novikov, Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 2 Article 024104
We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with the local moment tensor potential (MTP) and demonstrate that they ...
Added: July 22, 2026
Global optimization of atomic clusters via physically constrained tensor train decomposition
Sozykin K., Rybin N., Chertkov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 No. 22 Article 224111
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through tensor train (TT) decomposition. Our ...
Added: July 22, 2026
Kolmogorov Operators and Their Applications
Singapore: Springer, 2024.
Included in the following conference series: INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop Conference proceedings info: INdAM 2022 Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields. This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Existence and uniqueness results for strongly degenerate McKean-Vlasov equations with rough coefficients
Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...
Added: July 17, 2026
О сильных решениях многомерных СДУ с диагональными матрицами диффузии
Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304
Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...
Added: July 17, 2026
Improving Differential Equation Solving in Compact Language Models via Activation Steering and Reinforcement Learning
Surkov A., Ignatenko V., Koltcov Sergei, Computers, Materials and Continua 2026
Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without ...
Added: July 8, 2026
Современные методы теории краевых задач. Понтрягинские чтения XXXVII.
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронежская зимняя матаматическая школа С. Г. Крейна - 2026.
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,  включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Comparative Study of Training Methods and Architectures of Echo State Networks
Androsov I., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3 P. 87–114
This paper examines echo state networks (ESNs), one of the most prevalent approaches to implementing reservoir computing. An ESN consists of a recurrent neural network with fixed (untrained) weights and a readout layer that is typically linear and trainable. This approach enables the creation of energyefficient and computationally efficient neural networks capable of real-time learning. However, since ...
Added: May 26, 2026
Об изоморфизме задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Доклады Российской академии наук. Математика, информатика, процессы управления, том 527
М.: ФГБУ «Российская академия наук», 2025.
СПЕЦИАЛЬНЫЙ ВЫПУСК: ТЕХНОЛОГИИ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА И МАШИННОГО ОБУЧЕНИЯ ...
Added: November 27, 2025
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit