Wednesday, May 29, 2024

2024-06-03 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 박사논문심사:

by ()

2024-06-04 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 박사논문심사:

by ()

2024-05-30 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사:

by 채석주()

2024-06-05 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 계산수학 세미나: Efficient and Robust Multiphysics Simulation: A uniform framework for fluid dynamics in porous media

by 이슬잎()

This talk presents a uniform framework for computational fluid dynamics in porous media based on finite element velocity and pressure spaces with minimal degrees of freedom. The velocity space consists of linear Lagrange polynomials enriched by a discontinuous, piecewise linear, and mean-zero vector function per element, while piecewise constant functions approximate the pressure. Since the fluid model in porous media can be seen as a combination of the Stokes and Darcy equations, different conformities of finite element spaces are required depending on viscous parameters, making it challenging to develop a robust numerical solver uniformly performing for all viscous parameters. Therefore, we propose a pressure-robust method by utilizing a velocity reconstruction operator and replacing the velocity functions with a reconstructed velocity. The robust method leads to error estimates independent of a pressure term and shows uniform performance for all viscous parameters, preserving minimal degrees of freedom. We prove well-posedness and error estimates for the robust method while comparing it with a standard method requiring an impractical mesh condition. We finally confirm theoretical results through numerical experiments with two- and three-dimensional examples and compare the methods' performance to support the need for our robust method.

2024-05-29 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by ()

Post-critically finite (PCF) rational maps are a fascinating class of dynamical systems with rich mathematical structures. In this minicourse, we explore the interplay between topology, geometry, and dynamics in the study of PCF rational maps. [Lecture 3: Geometry of PCF rational maps] Geometry of PCF rational maps The topological models for PCF rational maps we discuss define canonical quasi-symmetric classes of metrics on their Julia sets. We investigate the conformal dimensions of Julia sets, which measure their geometric complexity and provide insights into the underlying dynamics. Through this exploration, we uncover the intricate relationship between the topology, geometry, and dynamics of PCF rational maps.

2024-05-29 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by ()

(John Hubbard's Mini-course: Lecture 3)

2024-06-04 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Semi-strong colourings of hypergraphs

by Jane Tan(University of Oxford)

A vertex colouring of a hypergraph is $c$-strong if every edge $e$ sees at least $\min\{c, |e|\}$ distinct colours. Let $\chi(t,c)$ denote the least number of colours needed so that every $t$-intersecting hypergraph has a $c$-strong colouring. In 2012, Blais, Weinstein and Yoshida introduced this parameter and initiated study on when $\chi(t,c)$ is finite: they showed that $\chi(t,c)$ is finite whenever $t \geq c$ and unbounded when $t\leq c-2$. The boundary case $\chi(c-1, c)$ has remained elusive for some time: $\chi(1,2)$ is known to be finite by an easy classical result, and $\chi(2,3)$ was shown to be finite by Chung and independently by Colucci and Gyárfás in 2013. In this talk, we present some recent work with Kevin Hendrey, Freddie Illingworth and Nina Kamčev in which we fill in this gap by showing that $\chi(c-1, c)$ is finite in general.

2024-05-31 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 6

by 이제학(KAIST)

This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.

2024-05-31 / 15:00 ~ 16:00

편미분방정식 통합연구실 세미나 - 편미분방정식: An optimal transport approach to the interface dynamics of supercooled water freezing into ice.

by 김영헌()

We discuss how optimal transport, which is a theory for matching different distributions in a cost effective way, is applied to the supercooled Stefan problem, a free boundary problem that describes the interface dynamics of supercooled water freezing into ice. This problem exhibits a highly unstable behaviour and its mathematical study has been limited mostly to one space dimension, and widely open for multi-dimensional cases. We consider a version of optimal transport problem that considers stopping of the Brownian motion, whose solution is then translated into a solution to the supercooled Stefan problem in general dimensions.

2024-05-31 / 14:00 ~ 16:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by (KAIST 수리과학과 & IBS 의생명수학그룹)

"Data driven governing equations approximation using deep neural networks", Journal of Computational Physics (2019) will be discussed in this Journal Club. We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation approximation. We demonstrate that the ResNet block can be considered as a one-step method that is exact in temporal integration. We then present two multi-step methods, recurrent ResNet (RT-ResNet) method and recursive ReNet (RS-ResNet) method. The RT-ResNet is a multi-step method on uniform time steps, whereas the RS-ResNet is an adaptive multi-step method using variable time steps. All three methods presented here are based on integral form of the underlying dynamical system. As a result, they do not require time derivative data for equation recovery and can cope with relatively coarsely distributed trajectory data. Several numerical examples are presented to demonstrate the performance of the methods. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact jaekkim@kaist.ac.kr if you first come IBS to get permission to enter IBS building.

2024-05-31 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 계산수학 세미나: PDEformer: Towards a Foundation Model for Solving Parametric PDEs and Beyond

by ()

Deep learning has emerged as a dominant approach in machine learning and has achieved remarkable success in various domains such as computer vision and natural language processing. Its influence has progressively extended to numerous research areas within the fields of science and engineering. In this presentation, I will outline our work on the design and training of a foundation model, named PDEformer, which aims to serve as a flexible and efficient solver across a spectrum of parametric PDEs. PDEformer is specifically engineered to facilitate a range of downstream tasks, including but not limited to parameter estimation and system identification. Its design is tailored to accommodate applications necessitating repetitive solving of PDEs, where a balance between efficiency and accuracy is sought. This is a joint workshop with the Serabol program.

2024-05-31 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Dynamical Billiard and a long-time behavior of the Boltzmann equation in general 3D toroidal domains

by 고경훈()

In this talk, we consider the Boltzmann equation in general 3D toroidal domains with a specular reflection boundary condition. So far, it is a well-known open problem to obtain the low-regularity solution for the Boltzmann equation in general non-convex domains because there are grazing cases, such as inflection grazing. Thus, it is important to analyze trajectories which cause grazing. We will provide new analysis to handle these trajectories in general 3D toroidal domains.

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