Applied & Computational Mathematics · Caltech
Dohyeon Kim 김도연 (金度延)
I am a PhD candidate in Applied and Computational Mathematics at the California Institute of Technology, advised by Professor Franca Hoffmann.
I began research in mean-field limits, interacting particle systems, and collective dynamics in May 2023, when I started working with Professor Hoffmann. Previously, until the end of 2022, I was advised by Professor Oscar Bruno on high-performance numerical methods for PDEs, which shaped my appreciation for both analytical structure and computational performance.
My current research applies these ideas to optimization and sampling. I use stochastic analysis and partial differential equations to understand stability, long-time behavior, and quantitative propagation of chaos.
Pasadena, California
Research
How do the collective dynamics of many interacting particles approximate a nonlinear equation, and how accurately can this approximation hold over long times? I investigate these questions for stochastic optimization and sampling methods, including consensus-based algorithms, particle swarm optimization, and Stein variational gradient descent.
Publications & preprints
Authors of all works in this section are listed alphabetically.
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Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD
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Long-time Stability and Convergence of Particle Swarm Optimization
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Uniform-in-time propagation of chaos for Second-Order Consensus-Based Optimization
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Uniform-in-time propagation of chaos for Consensus-Based Optimization
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MirrorCBO: A consensus-based optimization method in the spirit of mirror descent
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Mono-cluster flocking and uniform-in-time stability of the discrete Motsch–Tadmor model
Manuscripts in preparation 3
Further details and preprints will be shared soon.
Long-Time Behavior of Continuous-Time Consensus-Based Sampling
Solo work
Refined Long-Time Asymptotics for Variants of Consensus-Based Optimization
With Wuchen Li and Franca Hoffmann
Mean-Field Well-Posedness and Convergence Guarantees for Localized Consensus-Based Sampling
With Arne Bouillon, Kathrin Hellmuth, and Franca Hoffmann
Talks & visits
Upcoming
Variational Methods for Evolution
Mathematisches Forschungsinstitut Oberwolfach, Germany
Invited participant
Selected talks & visits
Research visit · BICMR, Peking University
Beijing, China · Hosted by Prof. Zhenfu Wang
Talk in Prof. Zhenfu Wang’s group seminar
Interacting Particle Systems and Their Applications
Institute for Mathematical Sciences, National University of Singapore
Invited speaker
Jun–Jul 2026
Uniform-in-time Propagation of Chaos for First- and Second-Order CBO
BIRS–IASM Workshop on Interacting Particle Systems · Hangzhou, China
Invited talk · Virtual
(Slides under revision; will be uploaded in June 2027)
Uniform-in-time Propagation of Chaos for Consensus-Based Optimization
SIAM Conference on Uncertainty Quantification · Minneapolis, Minnesota
May 2025
Uniform-in-time Mean Field Limit for Consensus-Based Optimization (CBO)
SIAM Conference on Applications of Dynamical Systems · Denver, Colorado
Session co-organizer & speaker
Co-organized with Nicolás García Trillos (UW–Madison), Sixu Li (UW–Madison), Claudia Totzeck (University of Wuppertal), and Yuhua Zhu (UCLA).
Sep 2024
Uniform-in-time Mean Field Limit for Consensus-Based Optimization (CBO)
Junior Kinetic Theory Workshop · Yonsei University
Invited talk
Jul 2024
Uniform-in-time Mean Field Limit for Consensus-Based Optimization (CBO)
9th European Congress of Mathematics · Seville, Spain
Invited talk
A full list of talks, posters, and workshops is in my CV.
Teaching & mentoring
Teaching at Caltech
Teaching assistantships, including guest lectures as noted.
Selected anonymous student comments from Caltech’s Teaching Quality Feedback Reports (TQFR).
- Spring 2026
ACM 270 Particles in Motion—Mathematical Modelling Across Scales
Instructor: Professor Kathrin Hellmuth
Developed lecture notes and delivered two 1.5-hour lectures on mean-field limits and propagation of chaos. Held weekly office hours and developed and graded homework problems.
April 28 · Lecture 1: Dobrushin’s estimate
April 30 · Lecture 2: Kac’s chaos and the BBGKY hierarchy
These lecture notes are in draft form and will be posted once finalized.
“Doh Yeon is great at resolving any confusion during the lecture, helping everyone move forward at a good pace. Again, it is impressive how much information was delivered in the Mean Field Theory lectures, with respect to the time constraints.”
Anonymous student · ACM 270, Spring 2026 · TQFR View TA evaluation · Spring 2026
Anonymous student feedback from Caltech TQFR. Course heading and my TA evaluation cropped from the same report. Click the image to enlarge. - Winter 2026
ACM 95/100A Introductory Methods of Applied Mathematics for the Physical Sciences
Instructor: Professor Konstantin Zuev
Held weekly office hours and graded homework problems and exams.
- Winter 2025
ACM 256 Optimal Transport
Instructors: Professors Franca Hoffmann and Ricardo Baptista
Held weekly office hours and graded homework problems.
View TA evaluation · Winter 2025
Anonymous student feedback from Caltech TQFR · ACM 256, Winter 2025. Click the excerpt to enlarge. - Winter 2024
ACM 95/100A Introductory Methods of Applied Mathematics for the Physical Sciences
Instructor: Professor Franca Hoffmann
Held weekly office hours and graded homework problems and exams.
“She was very supportive, always open to questions, well prepared for any question, and kind to explain concepts. She was the best to clarify doubts!”
Anonymous student · ACM 100A, Winter 2024 · TQFR View TA evaluation · ACM 100A, Winter 2024
Anonymous student feedback from Caltech TQFR · ACM 100A, Winter 2024. Click the excerpt to enlarge. - Fall 2023
CMS/ACM 117 Probability Theory and Computational Mathematics
Instructor: Professor Joel Tropp
Graded weekly homework problems and exams.
“Extremely responsible, clear and effective.”
Anonymous student · CMS/ACM 117, Fall 2023 · TQFR “Doh Yeon was amazing and helpful, and clearly knew the material and how to explain it to students.”
Anonymous student · CMS/ACM 117, Fall 2023 · TQFR View TA evaluation · Fall 2023
Anonymous student feedback from Caltech TQFR. Course heading and my TA evaluation cropped from the same report. Click the image to enlarge. - Winter 2023
ACM 105 (now ACM 107b) Applied Real and Functional Analysis
Instructor: Professor Oscar Leong
Delivered two 1.5-hour lectures on the Hahn–Banach theorem and the open mapping and closed graph theorems. Held weekly office hours and graded homework problems and exams.
“Doh Yeon is one of the best TAs I have ever encountered.”
Anonymous student · ACM 105, Winter 2023 · TQFR “Dohyeon was very helpful during office hours, I wouldn't have managed to get through the course without her help.”
Anonymous student · ACM 105, Winter 2023 · TQFR View written feedback · Winter 2023
Anonymous written feedback from Caltech TQFR. Course heading and written comments excerpted from the same report. Click the image to enlarge. - Fall 2022
CMS/ACM 117 Probability Theory and Stochastic Processes
Instructor: Professor Joel Tropp
Held weekly office hours, wrote problem-set solutions, and graded homework problems and exams.
“She gave me sufficient hints over piazza and in office hours, and was always encouraging and sympathetic when we got stuck.”
Anonymous student · CMS/ACM 117, Fall 2022 · TQFR View TA evaluation · Fall 2022
Anonymous student feedback from Caltech TQFR. Course heading and my TA evaluation cropped from the same report. Click the image to enlarge.
Mentoring
In collaboration with Professor Franca Hoffmann, I have mentored Ritvik Teegavarapu on convergence guarantees for particle swarm optimization through Caltech’s Summer Undergraduate Research Fellowships program, beginning in May 2024. Ritvik received the SOCAMS Best Poster Award (2025) and Caltech’s George W. and Bernice E. Green Memorial Prize, a research award (2026). He began his PhD with Professor Kavita Ramanan at Brown University in fall 2026, and our collaboration on annealed consensus-based optimization and sampling continues.
Background
Education
California Institute of Technology
PhD in Applied and Computational Mathematics, 2021–2027 (expected)
Advisor: Franca HoffmannYonsei University
BBA in Business Management; BS and MS in Mathematics
Highest Distinction · Valedictorian
Master’s advisor: Seick KimColumbia University
One-year undergraduate study abroad
Service
- Referee: SIAM Journal on Optimization (SIOPT); Mathematical Models and Methods in Applied Sciences (M3AS).
- Caltech SIAM Student Chapter: President, 2025–26; committee member, 2026–27.
- Womxn in EAS, Caltech: Committee member, 2024–present.
- SIAM Dynamical Systems 2025: Co-organized the minisymposium series “Collective Dynamics in Multi-Agent Systems: Advances in Learning and Optimization.”
More
Before joining Caltech, I received a BBA in Business Management and a BS in Mathematics, summa cum laude, from Yonsei University, where I was also the valedictorian. I began in business, but my first mathematics course in junior year left me wanting to learn more. I added a second major and took advanced courses in real analysis, PDEs, topology, and abstract algebra, initially out of curiosity. In my final semester, I decided to pursue mathematics in graduate school.
For more about my path into mathematics, the books I live with, and life outside research, visit Others. My CV has further academic details.