Sunday, May 26, 2024

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

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: tba

by ()

tba

2024-05-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Three-way online correlated selection

by 신용호(연세대)

Two-way online correlated selection (two-way OCS) is an online algorithm that, at each timestep, takes a pair of elements from the ground set and irrevocably chooses one of the two elements, while ensuring negative correlation in the algorithm's choices. OCS was initially invented by Fahrbach, Huang, Tao, and Zadimoghaddam (FOCS 2020, JACM 2022) to break a natural long-standing barrier in edge-weighted online bipartite matching. They posed two open questions, one of which was the following: Can we obtain n-way OCS for $n >2$, in which the algorithm can be given $n >2$ elements to choose from at each timestep? In this talk, we affirmatively answer this open question by presenting a three-way OCS which is simple to describe: it internally runs two instances of two-way OCS, one of which is fed with the output of the other. Contrast to its simple construction, we face a new challenge in analysis that the final output probability distribution of our three-way OCS is highly elusive since it requires the actual output distribution of two-way OCS. We show how we tackle this challenge by approximating the output distribution of two-way OCS by a flatter distribution serving as a safe surrogate. This is joint work with Hyung-Chan An.

2024-05-28 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 정수론:

by 이태영()

The finite quotient groups of étale fundamental groups of algebraic curves in positive characteristic are precisely determined, but without explicit construction of quotient maps, by well-known results of Raynaud, Harbater and Pop, previously known as Abhyankar's conjecture. Katz, Rojas León and Tiep have been studying the constructive side of this problem using certain "easy to remember" local systems. In this talk, I will discuss the main results and methods of this project in the case of a specific type of local systems called hypergeometric sheaves.

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.

2024-05-28 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 강경근(연세대학교)

Weak discuss existence of singular solutions for Stokes and the Navier-Stokes equations in the half-space. We construct their solutions whose normal derivatives are unbounded for the Stokes and Navier-Stokes equations near boundary away from support of singular data.

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