PDE & AI Lab at Yonsei

The PDE & AI Lab, launched in March 2026 at Yonsei University, studies mathematical theory and algorithms at the intersection of partial differential equations, optimization, and artificial intelligence. Our current interests include 

• Optimal Transport (see Dohyun's recent talk and 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, University of California, Los Angeles
  B.S in Mathematical Sciences, B.A. in Economics, Seoul National University
  Research Interests:
  Partial Differential Equations & Applied Mathematics (Gradient Flows, Optimization, Optimal Transport)
  Theory of Machine Learning (Mathematical Analysis of Generative Models, Applications of Gradient Flows in ML)
  
  

Postdoctoral Fellows

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

• Dr. Pilgyu Jung (2026.09 - )
  Ph.D. in Mathematics, Korea University
  Bachelor of Business Administration, B.S in Financial Engineering (Self-designed Transdisciplinary Studies), Sungkyunkwan University
  Research Interests: Partial Differential Equations, Optimal Transport, Applications of Wasserstein Barycenters

Graduate Students

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

• Junyoung Hwang (Ph.D./M.S. Integrated Program, 2026.09 - )
  B.S in Mathematics, University of Seoul
  Research Interests: Geometric Flows

Undergraduate Interns

• Sewon Kim, University of Seoul (2024. 09 - )
  Research Interests: Bilevel Optimization

• Juyeon Cho, Yonsei University (2026 Summer)

• Minseok Kang, University of Seoul (2026 Summer)

• Sugeun Lee, Yonsei University (2026 Summer)

• Woosung Yoon, University of Seoul (2026 Summer)

Graduate Students Hiring

• I am looking for motivated graduate students interested in partial differential equations, machine learning, and optimization. The current research interests include the following:
  - Partial Differential Equations, Optimization, Optimal Transport
  - Theory of Machine Learning, Mathematical Analysis of Generative Models (Diffusion Models, Transformers)

• Applicants from all academic backgrounds—including, but not limited to, Mathematics, Statistics, AI, Computer Science, Electrical Engineering, Physics, and other engineering disciplines—are welcome, provided they have a good foundation in mathematics.

• If you are interested in joining our PDE & AI group at Yonsei University, please contact me with your transcript and a short paragraph describing your research interests.

Postdoctoral Fellowship

• I have a couple of postdoctoral positions available.

Undergraduate Students Internship

• Our department, the School of Mathematics & Computing (Computational Science & Engineering), has a well-established summer/winter internship program for undergraduate students. Students from all majors are welcome to apply, including those from universities around the world. In other words, applicants do not need to be undergraduate students at Yonsei University.

• For application details, please visit https://cseurpyonsei.weebly.com/admission.html. Applications are typically submitted in May for summer internships and in November for winter internships. If you have any questions, please contact me or csedept@yonsei.ac.kr.

Grants

• National Research Foundation of Korea, 2026 - 2031 (as a Co-PI, No. RS-2026-25613008)
  한국연구재단, 차세대 AI+S&T 기반기술 개발(R&D) - 수학적 원리에 기반한 차세대 인공지능 구조 연구, 2026.07.01-2031.06.30, 총 연구비: 50억 원
  과제명: “트랜스포머와 다음 토큰 예측을 넘어“: 수학적 보장 기반 계층적 스펙트럼 상태공간 모델 및 통합 학습 알고리즘 연구

• 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)