Monday, March 20, 2023

2023-03-27 / 16:00 ~ 17:00

by Cho Sungwoong(Stochastic Analysis & Application Research Center)

Fast and accurate predictions for complex physical dynamics are a big challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in the real-world problems. The deep operator network (DeepONet) has recently been proposed as a framework for learning nonlinear mappings between function spaces. However, the DeepONet requires many parameters and has a high computational cost when learning operators, particularly those with complex (discontinuous or non-smooth) target functions. In this study, we propose HyperDeepONet, which uses the expressive power of the hypernetwork to enable learning of a complex operator with smaller set of parameters. The DeepONet and its variant models can be thought of as a method of injecting the input function information into the target function. From this perspective, these models can be viewed as a special case of HyperDeepONet. We analyze the complexity of DeepONet and conclude that HyperDeepONet needs relatively lower complexity to obtain the desired accuracy for operator learning. HyperDeepONet was successfully applied to various operator learning problems using low computational resources compared to other benchmarks.

2023-03-20 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

The standard approach to problem-solving in physics consists of identifying state variables of the system, setting differential equations governing the state evolution, and solving the obtained. The behavior of the system for different values of parameters can be examined only as a fourth step. On the contrary, the modern approach to studying dynamical systems relies on Morphological/Topological analysis which alleviates the necessity for the explicit solution of differential equations. The stability analysis of the parabolic swing will demonstrate the merit of such an approach. It will be shown how to construct a qualitatively correct model of system dynamics that is surprisingly quantitatively correct as well. The sudden (catastrophic) change in the swing’s stability, caused by a slight change in the critical value of system parameters, will be linked to the drastic topological change of the corresponding phase-space portraits. It will be shown that for a system’s parameters close to critical ones, the system’s behavior is identical to a specific simple universal prototype given by catastrophe theory. A short survey of the simplest elementary catastrophes will be given that represents the basis for applying catastrophe theory in other fields of science.

2023-03-27 / 16:00 ~ 18:00

IBS-KAIST 세미나 - IBS-KAIST 세미나: Mini-course on pluripotential theory and complex Monge-Ampere equations

by Sławomir Kolodziej(Jagiellonian University)

TBA

2023-03-24 / 14:00 ~ 16:00

IBS-KAIST 세미나 - IBS-KAIST 세미나: Mini-course on pluripotential theory and complex Monge-Ampere equations

by Sławomir Kolodziej(Jagiellonian University)

TBA

2023-03-23 / 16:00 ~ 18:00

IBS-KAIST 세미나 - IBS-KAIST 세미나: Mini-course on pluripotential theory and complex Monge-Ampere equations

by Sławomir Kolodziej(Jagiellonian University)

TBA

2023-03-24 / 09:00 ~ 10:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by ()

Modeling mass or heat transfer near a wall is of broad interest in various fluid flows. Specifically, in cardiovascular flows, mass transport near the vessel wall plays an important role in cardiovascular disease. However, due to very thin concentration boundary layers, accurate computational modeling is challenging. Additionally, experimental approaches have limitations in measuring near-wall flow metrics such as wall shear stress (WSS). In this talk, first, I will briefly review the complex flow physics near the wall in diseased vascular flows and introduce the concept of WSS manifolds in near-wall transport. Specifically, I will talk about stable and unstable manifolds calculated for a surface vector field. Next, I will discuss reduced-order data assimilation modeling as well as physics-informed neural network (PINN) approaches for obtaining WSS from measurement data away from the wall. Finally, I present a boundary-layer PINN (BL-PINN) approach inspired by the classical perturbation theory and asymptotic expansions to solve challenging thin boundary layer mass transport problems. BL-PINN demonstrates how classical theoretical approaches could be replicated in a deep learning framework.

2023-03-24 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 신원용(연세대학교)

그래프 신경망 (GNN: graph neural network)은 그래프에서 높은 표현 능력과 함께 특징 정보를 추출하는 방법론으로 학계와 산업체에서 최근 폭발적인 관심을 받고 있다. 본 세미나에서는 그래프 신경망의 개요 및 주요 동작 원리를 다룬다. 구체적으로, message passing의 원리를 이해하고 state-of-the-art 알고리즘에서 사용한 다양한 message passing 함수를 소개한다. 그래프 신경망을 활용한 다양한 downstream 응용 문제들이 존재하지만, 본 세미나에서는 근본적인 그래프 마이닝 문제 중 하나인 네트워크 정렬 (network alignment)으로의 적용을 다룬다. 네트워크 정렬 문제를 정의하고, 기존 연구 결과물들을 요약하고 한계점에 대해 설명한다. 이를 바탕으로 발표자 연구실에서 제안한 그래프 신경망을 활용한 새로운 점진적 네트워크 정렬 방법을 소개한다. 마지막으로, 그래프 신경망을 사용해 해결할 수 있는 다양한 실세계 응용 문제를 공유하고 토의한다.

2023-03-21 / 10:30 ~ 11:30

SAARC 세미나 - SAARC 세미나: Determinantal expressions for eigenvalue statistics of random matrices

by 정성우 박사(MIT 수학과)

We present new (mostly determinantal) expressions for various eigenvalue statistics in random matrix theory. Whenever the eigenvalue $n$-point correlation function is given in terms of $n \times n$ determinants with some kernel, we propose a new kernel that gives the $n$-point correlation function of the eigenvalues conditioned on the event of some eigenvalues already existing at fixed positions. Using such new kernels we obtain determinantal expressions for the joint densities of the $k$ largest eigenvalues, probability density function of the $k$-th largest eigenvalue, density of the first eigenvalue spacing, and many more. Our formulae is highly amenable to numerical computation through the method proposed by Bornemann (2008).

2023-03-20 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 계산수학 세미나: Fifty three matrix factorizations, symmetric spaces and generalized Cartan decomposition

by 정성우 박사(MIT 수학과)

Symmetric spaces from Lie theory and differential geometry are often represented by special set of structured matrices. The Cartan decomposition and its generalization of symmetric spaces and classical Lie groups recover many of the known matrix factorizations in numerical linear algebra, such as the singular value decomposition, CS decomposition, generalized SVD and many more. We discuss a blueprint for generating fifty-three matrix factorizations from the generalized Cartan decomposition, most of which appear to be new. The underlying mathematics may be traced back to Cartan (1927), Harish-Chandra (1956), and Flensted-Jensen (1978). This is joint work with Alan Edelman.

2023-03-24 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such post-transcriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA post-transcriptionally will always increase rather than decrease gene expression noise when the silencing of mRNA also increases its degradation as is expected for microRNA interactions with mRNA. In that regime we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression

2023-03-24 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Many questions in everyday life as well as in research are causal in nature: How would the climate change if we lower train prices or will my headache go away if I take an aspirin? Inherently, such questions need to specify the causal variables relevant to the question and their interactions. However, existing algorithms for learning causal graphs from data are often not scaling well both with the number of variables or the number of observations. This talk will provide a brief introduction to causal structure learning, recent efforts in using continuous optimization to learn causal graphs at scale and systematic approaches for causal experimental design at scale.

2023-03-23 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Problems in the mathematical fluid dynamics

by ()

In this lecture we introduce some challenging problems in the mathematical fluid mechanics. Although fluid mechanics is one of the most important physical phenomena we experience in everyday life, and has been studied for long time in history by top class mathematicians, still there are many problems which are open even at the fundamental level. We explain these problems and briefly review some of the recent progress.

2023-03-23 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 심병수(카이스트)

In this seminar, I will provide an overview of diffusion generative models, inverse problems, and their applications in solving such problems. Furthermore, I will present a novel interpretation of diffusion generative models and their translation to inverse problems. In collaboration with Hyungjin Chung and Dohoon Ryu, we propose that when data lies in a low-dimensional structure, the set of data with intermediate noise represents the interpolating manifold between the data manifold and the hypersphere of pure noise. Our new method, which respects this geometry, outperforms previous methods, and we provide experimental results as proof of concept.

Events for the 취소된 행사 포함