Friday, March 24, 2023

2023-03-31 / 12:00 ~ 13:00

by ()

Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for highdimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI) for high-dimensional inference tasks. By reframing the setup of B-PINNs as a traditional Bayesian inverse problem, we can take advantage of EKI’s key features: (1) gradient-free, (2) computational complexity scales linearly with the dimension of the parameter spaces, and (3) rapid convergence with typically O(100) iterations. We demonstrate the applicability and performance of the proposed method through various types of numerical examples. We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost. These findings suggest that our proposed approach has great potential for uncertainty quantification in physics-informed machine learning for practical applications.

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

IBS-KAIST 세미나 - 수리생물학:

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.

2023-03-28 / 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)

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

2023-03-24 / 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.

2023-03-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: On the maximum number of edges in k-critical graphs

by Tianchi Yang(National University of Singapore)

In this talk, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is k, but any proper subgraph has a chromatic number less than k. The problem remains open for any integer k ≥ 4. Our presentation will showcase an improvement on previous results achieved by employing a combination of extremal graph theory and structural analysis. We will introduce a key lemma, which may be of independent interest, as it sheds light on the partial structure of dense k-critical graphs. This is joint work with Cong Luo and Jie Ma.

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.

2023-03-30 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

We will first introduce Homogeneous dynamics, especially the mixing property of flows on spaces of hyperbolic nature. We will then survey applications of homogeneous dynamics to various problems in Number theory. (Part of the talk is based on joint work with Keivan Mallahi-Karai and Jiyoung Han.)

Events for the 취소된 행사 포함