报  告  人：Evgeny Burnaev教授    单  位：斯科尔科沃科学技术研究院（俄罗斯）
会 议 地 点：活动中心320              报告时间：2025年4月9日（星期三）14:00-15:00
邀   请  人：张伟男教授                  主 持 人：张伟男教授

From stochastic differential equations to the Monge-Kantorovich problem and back: the path to Generative AI?

Abstract: A.N. Kolmogorov is the greatest mathematician of the XX century, the founder of modern probability theory, who also laid the foundations of the theory of Markov random processes in continuous time. These results, which significantly impacted the development of applied methods of signal processing, filtering, modeling, and processing of financial data, were again in the spotlight due to the development of artificial intelligence and its applications in the 21st century.

Indeed, to solve such important applied tasks as image super-resolution, text-to-speech synthesis, image generation based on text descriptions, etc., effective generative modeling methods are required to generate objects from the distribution represented by a sample of examples. Recent achievements in the field of generative modeling are based on diffusion models and use the mathematical foundations laid down in the last century by A.N. Kolmogorov and his followers.

I will talk about modern approaches to generative modeling based on the diffusion processes and on the solution to the Monge-Kantorovich problem. I will show the connection between the entropy-regularized Monge-Kantorovich problem and the problem of constructing a diffusion process with specific extreme properties. I will demonstrate applications of the corresponding algorithms based on various image processing problems.

Bio: Evgeny Burnaev is the Director of Skoltech Artificial Intelligence Center, Professor, Doctor of Physical and Mathematical Sciences, and a member of the Scientific Council of the AI Alliance.

His research interests focus on the mathematical foundations of generative AI and the development of predictive analytics technologies, including industrial applications. Between 2019 and 2025, Professor Burnaev published around 120 scientific papers, over 60 of which appeared in top-tier journals and A/A* AI-conferences (NeurIPS, ICML, CVPR, etc.). For the second consecutive year, he is listed among the top 2% of the world’s most cited researchers, according to Stanford University and Elsevier.

Previously, Evgeny led the Laboratory for Intelligent Data Analysis and Predictive Modeling at the Institute for Information Transmission Problems of the Russian Academy of Sciences (IITP RAS). In parallel, Evgeny collaborated with Huawei, Airbus, SAFT, IHI, Sahara Force India (Formula 1), and other industrial partners. These collaborations, ongoing since 2007, have given him extensive experience in deploying machine learning methods in real-world industrial systems.

Since 2021, Evgeny has headed Skoltech Applied AI Center — launched as part of the National “Digital Economy” Project with support from the Analytical Center under the Government of the Russian Federation and various industry partners. In late 2024, the center was rebranded as the Skoltech Artificial Intelligence Center, bringing together all existing university research groups and labs dedicated to AI technologies.

Among Professor Burnaev’s awards are the Moscow Government Award for Young Scientists in the category “Transmission, Storage,Processing, and Protection of Information,” the Yandex Ilya Segalovich Award in the “Scientific Supervisors” category, and numerous best paper honors (including research in esports and geometric data analysis). In 2024, he received the Government of the Russian Federation Award in Science and Technology, departmental insignia of the Autonomous non-profit organization «Digital Economy» for «Significant contribution to the development of scientific research in the field of artificial intelligence», departmental insignia of the Ministry of Economic Development of the Russian Federation «Gratitude of the Minister of Economic Development of the Russian Federation» for achievements in the development of Artificial Intelligence, as well as the Sber Science Award in the “Digital Universe” nomination.