Dohyeon Kim

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 theory, 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 tools from probability, partial differential equations, and kinetic theory to understand stability, long-time behavior, and quantitative propagation of chaos.

dohyeon@caltech.eduGoogle ScholarCurriculum vitae

Dohyeon Kim
PhD candidate · Caltech
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.

Manuscripts in preparation 4

Further details and preprints will be shared soon.

  • Long-time behavior of consensus-based sampling

    Solo work

  • Information-theoretic analysis of consensus-based optimization

    With Wuchen Li and Franca Hoffmann

  • Mean-field analysis of localized consensus-based sampling

    With Arne Bouillon, Kathrin Hellmuth, and Franca Hoffmann

  • Towards Convergence Guarantees for Particle Swarm Optimization

    With Ritvik Teegavarapu and Franca Hoffmann

Talks & visits

Upcoming

  • Interacting Particle Systems and Their Applications

    Institute for Mathematical Sciences, National University of Singapore

    Invited speaker

  • Research visit · BICMR, Peking University

    Beijing, China · Hosted by Prof. Zhenfu Wang

  • Variational Methods for Evolution

    Mathematisches Forschungsinstitut Oberwolfach, Germany

    Invited participant

Selected talks

  • 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)

  • Consensus-Based Optimization: When the Crowd Becomes Wise

    Caltech Three Minute Thesis (3MT) Competition

    Finalist

    To my knowledge, the first finalist from Mathematics or Applied & Computational Mathematics in at least three years.

    Video · Event

  • Uniform-in-time Propagation of Chaos for Consensus-Based Optimization

    SIAM Conference on Uncertainty Quantification · Minneapolis, Minnesota

    Slides (PDF)

  • May 2025

    Uniform-in-time Mean Field Limit for Consensus-Based Optimization (CBO)

    SIAM Conference on Applications of Dynamical Systems · Denver, Colorado

    Session organizer & speaker

  • 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.

  • Spring 2026

    ACM 270 Special Topics Course (Particles in Motion: Mathematical Modelling Across Scales)

    Developed lecture notes and delivered two lectures on mean-field limits and propagation of chaos on April 28 and 30, 2026.

    Held office hours and graded assignments.

    April 28 · Lecture 1: Dobrushin’s estimate

    April 30 · Lecture 2: Kac chaos and the BBGKY hierarchy

    These lecture notes are in draft form and will be posted once finalized.

  • Winter 2026 Winter 2024

    ACM 95/100A Introductory Methods of Applied Mathematics for the Physical Sciences

    Held office hours and graded assignments.

  • Winter 2025

    ACM 256 Special Topics Course (Optimal Transport)

    Held office hours and graded assignments.

  • Fall 2023 Fall 2022

    CMS/ACM 117 Probability Theory and Stochastic Processes

    Held office hours and graded assignments.

  • Winter 2023

    ACM 105 (now ACM 107b) Functional Analysis

    Delivered two lectures on the Hahn–Banach theorem and the open mapping and closed graph theorems.

    Held office hours and graded assignments.

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 a poster award at SOCAMS 2025 and began his PhD at Brown University in fall 2026.

Background

Education

  • California Institute of Technology

    PhD in Applied and Computational Mathematics, 2021–2027 (expected)
    Advisor: Franca Hoffmann

  • Yonsei University

    BBA in Business Management; BS and MS in Mathematics
    Highest Distinction · Valedictorian
    Master’s advisor: Seick Kim

  • Columbia 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.