报告题目：

The fundamental Principles of Generative AI

生成式人工智能的基本原理

报告时间：2026年4月10日 14：00

报告地点：大连理工大学开发区校区信息楼计算机广场报告厅

报告人：Dr. David Xianfeng Gu

报告内容（摘要）：

In this talk series, the fundamental mathematical principles of popular generative models will be explained in details, including Normalizing Flow (NF), Neural ODE (CNF), Flow Matching (FM) and Denoise Diffusion Probabilistic Models (DDPM). Their hypothesis, mathematical formulation, algorithmic details and performance analysis will be covered carefully. Furthermore, the optimal transportation model will be used to compare with these models, and explain their intrinsic bottlenecks and the improvement approaches. We also cover geometric variational optimal transportation method, prove the existence, uniqueness of the solution, give sufficient conditions for the existence of singularities, the global structure of the space of all OT mappings, and analyze the algorithmic challenges for Monte-Carlo OT method.

在本系列讲座中，将详细解释流行生成模型的基本数学原理，包括标准化流、神经常微分方程、流匹配和去噪扩散概率模型。将仔细涵盖它们的假设、数学公式、算法细节和性能分析。此外，将使用最优传输模型与这些模型进行比较，并解释其内在瓶颈和改进方法。我们还涵盖几何变分最优传输方法，证明解的存在性和唯一性，给出奇点存在的充分条件，所有最优传输映射空间的全局结构，并分析蒙特卡洛最优传输方法的算法挑战。

报告人简介：

Dr. David Xianfeng Gu is the Empire Innovation Professor in the Departments of Computer Science and Applied Mathematics at the State University of New York at Stony Brook. He earned his Bachelor's degree from Tsinghua University and his Master's and Ph.D. in Computer Science from Harvard University, where he was advised by Fields Medalist Professor Shing-Tung Yau. David is the major founder of an emerging interdisciplinary field: Computational Conformal Geometry, which combines different fields in modern mathematics, including low dimensional topology, differential geometry, Riemann surface theory and geometric PDE with computer science, to tackle fundamental problems in engineering and medical fields. David has generalized the Ricci flow theory, which has been used by Perelman to prove the famous Poincare conjecture in topology, to the discrete manifolds, and applied it for structured mesh generation. David also developed the geometric variational method to solve the optimal transport map, and applied it for generative AI. David has published tens of academic books, hundreds of papers published in the top conferences and journals in the fields. He has won several best paper awards, research awards, NSF Career award, outstanding off-sea scholar award, gold medal in applied mathematics in ICCM and many other awards. He is the chief editor and associate editors of several journals in discrete geometry and applied mathematics.

顾险峰博士是纽约州立大学石溪分校计算机科学与应用数学系的帝国创新教授。他于清华大学获得学士学位，并于哈佛大学获得计算机科学硕士和博士学位，师从菲尔兹奖得主丘成桐教授。顾险峰是一个新兴交叉领域——计算共形几何学的主要创始人，该领域将现代数学中的低维拓扑、微分几何、黎曼曲面理论和几何偏微分方程与计算机科学相结合，以解决工程和医学领域的基础问题。他将被佩雷尔曼用于证明拓扑学中著名庞加莱猜想的里奇流理论推广到离散流形，并将其应用于结构化网格生成。他还开发了几何变分方法来求解最优传输映射，并将其应用于生成式人工智能。顾险峰已出版数十本学术书籍，在顶级会议和期刊上发表了数百篇论文。他获得了多项最佳论文奖、研究奖、美国国家科学基金会职业奖、海外杰出学者奖、国际华人数学家大会应用数学金奖等众多奖项。他担任多本离散几何和应用数学期刊的主编和副主编。