40 citations · 209 across the 49 of their papers we have counts for
50 papers
Relativistic BGK model for gas mixtures
Byung-Hoon Hwang, Myeong-Su Lee, Seok-Bae Yun
Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results %\cite{Kremer,Kremer3,KP} in w…
Separable Physics-Informed Neural Networks
Junwoo Cho, Seungtae Nam, Hyunmo Yang +3
Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental lim…
Mathematical modeling of trend cycle: Fad, Fashion and Classic
Hyeong-Ohk Bae, Seung Yeon Cho, Jane Yoo +1
In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynami…
Inexact Online Proximal Mirror Descent for time-varying composite optimization
Woocheol Choi, Myeong-Su Lee, Seok-Bae Yun
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involv…
On the convergence result of the gradient-push algorithm on directed graphs with constant stepsize
Woocheol Choi, Doheon Kim, Seok-Bae Yun
Distributed optimization has recieved a lot of interest due to its wide applications in various fields. It consists of multiple agents that connected by a graph and optimize a tota…
Large amplitude problem of BGK model: Relaxation to quadratic nonlinearity
Gi-Chan Bae, Gyounghun Ko, Donghyun Lee +1
Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic f…
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
Seungchan Ko, Seok-Bae Yun, Youngjoon Hong
In this paper, we perform the convergence analysis of unsupervised Legendre--Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial different…
Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks
Junwoo Cho, Seungtae Nam, Hyunmo Yang +3
Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forward and inverse problems. While promising, the expensive computational costs to ob…
Physics-Informed Convolutional Transformer for Predicting Volatility Surface
Soohan Kim, Seok-Bae Yun, Hyeong-Ohk Bae +2
Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes opt…
PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers
Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong +2
With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed n…
BGK model for multi-component gases near a global Maxwellian
Gi-Chan Bae, Christian Klingenberg, Marlies Pirner +1
In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \cite{mixmodel} when the initial data is a…
The Shakhov model near a global Maxwellian
Gi-Chan Bae, Seok-Bae Yun
Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl…
A unified framework for distributed optimization algorithms over time-varying directed graphs
Woocheol Choi, Doheon Kim, Seok-Bae Yun
In this paper, we propose a framework under which the decentralized optimization algorithms suggested in \cite{JKJJ,MA, NO,NO2} can be treated in a unified manner. More precisely,…
Convergence results of a nested decentralized gradient method for non-strongly convex problems
Woocheol Choi, Doheon Kim, Seok-Bae Yun
We are concerned with the convergence of NEAR-DGD (Nested Exact Alternating Recursion Distributed Gradient Descent) method introduced to solve the distributed optimization prob…
Entropy production estimate for the ES-BGK model with the correct Prandtl number
Doheon Kim, Myeong-Su Lee, Seok-Bae Yun
In this paper, we establish the entropy-entropy production estimate for the ES-BGK model, a generalized version of the BGK model of the Boltzmann equation introduced for better app…
Relativistic BGK model for massless particles in the FLRW spacetime
Byung-Hoon Hwang, Ho Lee, Seok-Bae Yun
In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaitre-Robertson-Walker (FLRW…
On a relativistic BGK model for polyatomic gases near equilibrium
Byung-Hoon Hwang, Tommaso Ruggeri, Seok-Bae Yun
Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting mode…
The relativistic quantum Boltzmann equation near equilibrium
Gi-Chan Bae, Jin Woo Jang, Seok-Bae Yun
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent…
Stationary Flows of the ES-BGK model with the correct Prandtl number
Stephane Brull, Seok-Bae Yun
Ellipsoidal BGK model (ES-BGK) is a generalized version of the BGK model where the local Maxwellian in the relaxation operator of the BGK model is extended to an ellipsoidal Gaussi…
Conservative semi-Lagrangian schemes for kinetic equations Part I: Reconstruction
Seung Yeon Cho, Sebastiano Boscarino, Giovanni Russo +1
In this paper, we propose and analyse a reconstruction technique which enables one to design high-order conservative semi-Lagrangian schemes for kinetic equations. The proposed rec…
Conservative semi-Lagrangian schemes for kinetic equations Part II: Applications
Seung Yeon Cho, Sebastiano Boscarino, Giovanni Russo +1
In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic equations. They are based on the conservative reconstruction technique introduced in [S. Y…
Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules
Sebastiano Boscarino, Seung-Yeon Cho, Giovanni Russo +1
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knud…
Stationary BGK models for chemically reacting gas in a slab
Doheon Kim, Myeong-Su Lee, Seok-Bae Yun
We study the boundary value problem of two stationary BGK-type models - the BGK model for fast chemical reaction and the BGK model for slow chemical reaction - and provide a unifie…
Propagation of estimates for the Spatially Homogeneous Relativistic Boltzmann Equation
Jin Woo Jang, Seok-Bae Yun
In this paper, we prove the propagation of upper bounds for the spatially homogeneous relativistic Boltzmann equation for any . We consider the case of relativist…