PDE & AI Seminar at Yonsei
PDE & AI Seminar at Yonsei
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August 10, 2026
Talk 1: 3 - 4:30 pm
Speaker: Sewon Kim (University of Seoul)
Language: Korean
Title: TBA
Abstract: TBA
Talk 2: 4:50pm - 6:00 pm
Speaker: Dohyun Kwon (Yonsei University)
Title: A Fully First-Order Method for Bilevel Optimization
Language: Korean
Abstract: The problem of bilevel optimization has been the focus of extensive study in recent years. Although many optimization methods have been proposed to address bilevel problems, existing approaches often require potentially expensive calculations involving the Hessians of lower-level objectives. The primary technical challenge lies in tracking the lower-level solutions as upper-level variables change. We introduce a Fully First-order Stochastic Approximation method, which relies only on first-order gradient oracles. We also analyze the complexity of first-order methods under minimal assumptions and provide matching lower bounds. Toward the end of the talk, I will briefly discuss recent extensions, including a continuous-time perspective on bilevel problems, as well as related developments for tri-level optimization. This talk is based on joint work with Jeongyeol Kwon (Meta), Hanbaek Lyu, Stephen Wright, Robert Nowak (UW-Madison), Sewon Kim (University of Seoul), and Hyunwoo Lee (KIAS).
July 20, 2026
Talk 1: 3 - 4:30 pm
Speaker: Pilgyu Jung (Yonsei University)
Language: Korean
Title: TBA
Abstract: TBA
Talk 2: 4:50pm - 6:00 pm
Speaker: Dohyun Kwon (Yonsei University)
Language: Korean
Title: Optimal Transport: Discrete, Continuous, and Neural Perspectives
Abstract: Optimal transport provides a powerful framework for comparing, interpolating, and transforming probability distributions. This talk introduces optimal transport from three complementary perspectives: discrete, continuous, and neural. We first discuss the discrete viewpoint, beginning with Monge’s problem and Kantorovich’s relaxation, and explain how transport plans and Wasserstein distances arise in computational optimal transport. We then move to the continuous setting, where optimal transport maps, Kantorovich couplings, and Wasserstein gradient flows provide a geometric and variational description of probability measures. Finally, we discuss neural optimal transport and its role in modern generative modeling, including connections to Wasserstein generative models and learned transport maps. The goal of the talk is to highlight how optimal transport connects classical mathematical analysis, computational methods, and contemporary machine learning.
June 19, 2026 [Link]
Talk 1: 3:00 - 4:00 pm
Speaker: Ho Yun (EPFL)
Title: Gaussian Optimal Transport beyond Brenier’s Non-Degeneracy
Abstract: This talk presents an operator-algebraic approach to Gaussian Optimal Transport on separable Hilbert spaces. We completely describe the Monge and Kantorovich problems, without imposing any regularity assumptions on the covariances. Moving forward, this talk explains the dynamic paths that particles travel as they transition from the starting state to the target. Additionally, when using entropic regularization, we demonstrate that the solution is characterized as a straightforward shrinking of the correlation operator. We will conclude by discussing how this perspective leads to more efficient computational algorithms and connects different geometric views of these transport problems.
Talk 2: 4:00 - 5:00 pm
Speaker: Almond Stöcker (EPFL)
Title: Infinite-Dimensional Spherical Kernel Ridge Regression
Authors: Beatrice Matteo, Almond Stöcker, Shahin Tavakoli
Abstract: We introduce a new regression framework for nonlinear modeling of responses that lie on Hilbert spheres of not necessarily finite dimension. Unlike tangent space regression, which lifts all responses to a common tangent space, our approach estimates conditional Fréchet means with respect to the intrinsic distance on the manifold. A representer theorem yields a representation of the mean function in a linear predictor space - the tangent space at a reference point - and reduces the infinite-dimensional estimation problem to a finite-dimensional one, which can efficiently be solved using a BFGS algorithm with double low-rank approximation. We establish convergence rates and analyze the finite-sample behavior of our estimator, concluding with an application to density regression. A ready-to-use implementation is available in R.
June 18, 2026
Speaker: Joseph S. Kwon (Richard Morrow Endowed Chair and Professor, Chemical and Biomolecular Engineering at The Ohio State University)
Title: Hybrid Modeling of Chemical Processes: Integrating Physics with Machine Learning to Capture Missing Physics [Link]
June 1, 2026
Speaker: Hyunwoo Lee (KIAS, AI & Natural Sciences Center)
Title: Weight Initialization Methods for Neural Networks [Link]
May 28, 2026
Speaker: Jae-Hwan Choi (KIAS, School of Mathematics)
Title: Introduction to Infinite-Dimensional Probability Theory and Its Application to Optimal Transport [Link]
April 30, 2026
Speaker: Jun-Kee Jeon (KHU, Department of Applied Mathematics)
Title: Stochastic Control and Free Boundary Problem: Theory, Applications, and Computations [Link]
April 16, 2026
Speaker: Jiseok Chae (KAIST, Department of Mathematical Sciences / PDE&AI Lab at Yonsei)
Title: Constructing Convergent Methods for Minimax Optimization Problems [Link]
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