PDE & AI Lab at Yonsei

The PDE & AI Lab studies mathematical theory and algorithms at the intersection of partial differential equations, optimization, and artificial intelligence. Our current interests include 

• Optimal Transport (see this article), Partial Differential Equations (Dohyun's seminar talk regarding mean curvature flow)

• Optimization (Dohyun's YouTube video,  Korean)

• Machine Learning Theory, Generative Models (Dohyun's seminar talk(Korean) at KIAS regarding diffusion models)

We develop rigorous analytical tools for understanding machine learning problems and apply them to design and improve modern learning algorithms. See these keynote slides (English) or here (Korean) for more information.

Current Members

Principal Investigator

• Prof. Dohyun Kwon
  Ph.D. in Mathematics, UCLA, B.S in Mathematical Sciences, Seoul National University
  Research Interests: Theory of Machine Learning (Mathematical Analysis of Generative Models, Applications of Gradient Flows in ML), Partial Differential Equations & Applied Mathematics (Gradient Flows, Optimization, Optimal Transport)

Postdoctoral Fellows

• Dr. Jiseok Chae (2026.04 - )
  Ph.D., B.S. in Mathematical Sciences, KAIST
  Research Interests: Minimax Optimization Theory and Machine Learning Applications

Graduate Students

• Dohyeon Kwak (Ph.D. Program, 2025.09 - )
  M.S, B.S in Mathematics, Yonsei University
  Research Interests:  Physics-Informed Neural Network, Optimal Transport, Numerical Analysis

Undergraduate Interns

• Junyoung Hwang, University of Seoul (2026.03 - )

• Sewon Kim, University of Seoul (2024. 09 - )

Grants

• National Research Foundation of Korea, 2026 - 2031 (No. RS-2026-25488663)
  한국연구재단, 신진연구(유형B, 수학), 2026.03.01-2031.02.28, 총 연구비: 7억 원
  과제명: 생성모델 해석을 위한 최적 운송 연구 (Optimal Transport for the Analysis of Generative Models)

• 연세대학교, 미래선도연구사업, 2026-2029, 총 연구비: 1.5억 원
  과제명: 생성모델의 안정성과 제어 원리 연구 (Stability and Control Principles of Generative Models)

• Basic Research Laboratory, National Research Foundation of Korea, 2024 - 2027 (as a Co-I, No. RS-2024-00408003)
  한국연구재단, 글로벌 기초연구실 지원사업 (개척형, ICT/융합), 2024.08.01.-2027.04.30, 총 연구비: 13.75억 원
  과제명: 신뢰 가능한 파운데이션 모델을 위한 이론적 프레임워크 및 확장 가능한 개인화 솔루션 개발 (Developing Reliable Foundation Models with Theoretical Framework and Scalable Personalization)

• POSCO Science Fellowship, TJ Park Foundation, 2024 - 2025
  포스코 청암 재단, 포스코 사이언스 펠로십 (신진교수, 수학), 2024.01.01.-2026.12.31, 총  연구비: 1억 원
  과제명: 확률공간에서의 수렴성 연구와 생성 모델로의 응용  (Convergence in the Wasserstein space and its applications to generative models)

• National Research Foundation of Korea, 2023 - 2026 (No. RS-2023-00252516)
  한국연구재단, 개인기초연구 기본연구 (수학), 2023.06.01-2026.02.28, 총 연구비: 1.95억 원
  과제명: 편미분방정식의 기울기 흐름 구조를 활용한 경계 움직임 연구 (Analysis of interface dynamics via gradient flows in PDEs)