arXiv subjects

Jeongho Kim

Publications and source records attributed to Jeongho Kim.

At least 37 records · Page 2Linked to original sources

arXiv2025

Derivation of nonlinear aggregation-diffusion equation from a kinetic BGK-type equation

This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by Dolbeault et al. [Arch. Ration. Mech. Anal., 186, (2007), 133-158] and Addala and Tayeb [J. Hyperbolic Differ. Equ., 16, (2019), 131-156], which required bounded initial data, our work considers initial data that need not be bounded. We develop new techniques for handling weak entropy solutions that satisfy the natural bounds associated with the kinetic entropy inequality. Our proof employs the relative entropy method and various compactness arguments to establish the convergence and properties of these solutions.

math.AP↗

arXiv2025

Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type

We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg type, called the Navier-Stokes-Korteweg(NSK) system. Precisely, we show that the solution to the NSK system asymptotically converges to the composition of the rarefaction wave and shifted viscous-dispersive shock wave, under certain smallness assumption on the initial perturbation and strength of the waves. Our method is based on the method of $a$-contraction with shift developed by Kang and Vasseur \cite{KV16}, successfully applied to obtain contraction or stability of nonlinear waves for hyperbolic systems.

math.AP↗

arXiv2025

Asymptotic behavior toward viscous shock for impermeable wall and inflow problem of barotropic Navier-Stokes equations

We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider the two boundary problems: impermeable wall and inflow problems, where the velocity at the boundary is given as a constant state. For both problems, when the asymptotic profile determined by the prescribed constant states at the boundary and far-fields is a viscous shock, we show that the solution asymptotically converges to the shifted viscous shock profiles uniformly in space, under the condition that initial perturbation is small enough in $H^1$ norm. Since our method works on the physical variables, we do not require that the anti-derivative variables belong to $L^2$ space as in \cite{HMS03,MM99}. Moreover, for the inflow case, we remove the assumption $γ\le 3$ in \cite{HMS03}. Our results are based on the method of $a$-contraction with shifts, as the first extension of the method to the boundary value problems.

math.AP↗

arXiv2024

What to Preserve and What to Transfer: Faithful, Identity-Preserving Diffusion-based Hairstyle Transfer

Hairstyle transfer is a challenging task in the image editing field that modifies the hairstyle of a given face image while preserving its other appearance and background features. The existing hairstyle transfer approaches heavily rely on StyleGAN, which is pre-trained on cropped and aligned face images. Hence, they struggle to generalize under challenging conditions such as extreme variations of head poses or focal lengths. To address this issue, we propose a one-stage hairstyle transfer diffusion model, HairFusion, that applies to real-world scenarios. Specifically, we carefully design a hair-agnostic representation as the input of the model, where the original hair information is thoroughly eliminated. Next, we introduce a hair align cross-attention (Align-CA) to accurately align the reference hairstyle with the face image while considering the difference in their head poses. To enhance the preservation of the face image's original features, we leverage adaptive hair blending during the inference, where the output's hair regions are estimated by the cross-attention map in Align-CA and blended with non-hair areas of the face image. Our experimental results show that our method achieves state-of-the-art performance compared to the existing methods in preserving the integrity of both the transferred hairstyle and the surrounding features. The codes are available at https://github.com/cychungg/HairFusion

cs.CV↗

arXiv2024

TCAN: Animating Human Images with Temporally Consistent Pose Guidance using Diffusion Models

Pose-driven human-image animation diffusion models have shown remarkable capabilities in realistic human video synthesis. Despite the promising results achieved by previous approaches, challenges persist in achieving temporally consistent animation and ensuring robustness with off-the-shelf pose detectors. In this paper, we present TCAN, a pose-driven human image animation method that is robust to erroneous poses and consistent over time. In contrast to previous methods, we utilize the pre-trained ControlNet without fine-tuning to leverage its extensive pre-acquired knowledge from numerous pose-image-caption pairs. To keep the ControlNet frozen, we adapt LoRA to the UNet layers, enabling the network to align the latent space between the pose and appearance features. Additionally, by introducing an additional temporal layer to the ControlNet, we enhance robustness against outliers of the pose detector. Through the analysis of attention maps over the temporal axis, we also designed a novel temperature map leveraging pose information, allowing for a more static background. Extensive experiments demonstrate that the proposed method can achieve promising results in video synthesis tasks encompassing various poses, like chibi. Project Page: https://eccv2024tcan.github.io/

cs.CV↗

arXiv2024

Long-time behavior towards viscous-dispersive shock for Navier-Stokes equations of Korteweg type

We consider the so-called Naiver-Stokes-Korteweg(NSK) equations for the dynamics of compressible barotropic viscous fluids with internal capillarity. We handle the time-asymptotic stability in 1D of the viscous-dispersive shock wave that is a traveling wave solution to NSK as a viscous-dispersive counterpart of a Riemann shock. More precisely, we prove that when the prescribed far-field states of NSK are connected by a single Hugoniot curve, then solutions of NSK tend to the viscous-dispersive shock wave as time goes to infinity. To obtain the convergence, we extend the theory of $a$-contraction with shifts, used for the Navier-Stokes equations, to the NSK system. The main difficulty in analysis for NSK is due to the third-order derivative terms of the specific volume in the momentum equation. To resolve the problem, we introduce an auxiliary variable that is equivalent to the derivative of the specific volume.

math.AP↗

arXiv2023

StableVITON: Learning Semantic Correspondence with Latent Diffusion Model for Virtual Try-On

Given a clothing image and a person image, an image-based virtual try-on aims to generate a customized image that appears natural and accurately reflects the characteristics of the clothing image. In this work, we aim to expand the applicability of the pre-trained diffusion model so that it can be utilized independently for the virtual try-on task.The main challenge is to preserve the clothing details while effectively utilizing the robust generative capability of the pre-trained model. In order to tackle these issues, we propose StableVITON, learning the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model in an end-to-end manner. Our proposed zero cross-attention blocks not only preserve the clothing details by learning the semantic correspondence but also generate high-fidelity images by utilizing the inherent knowledge of the pre-trained model in the warping process. Through our proposed novel attention total variation loss and applying augmentation, we achieve the sharp attention map, resulting in a more precise representation of clothing details. StableVITON outperforms the baselines in qualitative and quantitative evaluation, showing promising quality in arbitrary person images. Our code is available at https://github.com/rlawjdghek/StableVITON.

cs.CV↗

arXiv2022

Automated CFD shape optimization of stator blades for the PediaFlow pediatric ventricular assist device

PediaFlow is a miniature mixed-flow ventricular assist device for neonates and toddlers. PediaFlow has a fully magnetically levitated rotor which improves biocompatibility, but the increased length of the rotor creates a long annular passage where fluid energy is lost. Therefore, a set of helical stator blades was proposed immediately after the impeller stage to remove the swirling flow and recover the dynamic head as static pressure. Automated computational fluid dynamics (CFD) shape optimization of the stator blades was performed to maximize pressure recovery at the operating point of 1.5 LPM and 16,000 RPM. Additionally, the effect on hemolysis and thrombogenicity was assessed using numerical modeling. The optimization algorithm favored fewer blades of greater length over a larger number of short blades. The ratio of wrap angle to axial length emerged as a key constraint to ensure the viability of a design. The best design had 2 blades and generated 73 mmHg of pressure recovery in an isolated stage. When re-introduced to the CFD simulation of the complete flow path, the added stator stage increased the pump head by 46% and improved the pump efficiency from 21.9% to 25.7% at the selected operating point. Automated CFD shape optimization combined with in silico evaluation of hemocompatibility can be an effective tool for exploring design choices and informing early development process.

physics.flu-dyn↗

arXiv2022

Large-time behavior of composite waves of viscous shocks for the barotropic Navier-Stokes equations

We study the large-time behavior of the 1D barotropic Navier-Stokes flow perturbed from Riemann data generating a composition of two shock waves with small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, towards a composition of two viscous shock waves as time goes to infinity, up to dynamical shifts. Especially, the strengths of the two waves can be chosen independently. This is the first result for the convergence to a composite wave of two viscous shocks with independently small amplitudes.

math.AP↗

arXiv2021

Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields

We present two types of the hydrodynamic limit of the nonlinear Schrödinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible and incompressible Euler system, coupled with the Chern-Simons equations and Poisson equation respectively, as the scaled Planck constant converges to 0. Our method is based on the modulated energy estimate. In the case of compressible limit, we observe that the classical theory of relative entropy method can be applied to show the hydrodynamic limit, with the additional quantum correction term. On the other hand, for the incompressible limit, we directly estimate the modulated energy to derive the desired asymptotic convergence.

math.AP↗

arXiv2021

Synthesis, electric-field induced phase transitions and memristive properties of spontaneously ion intercalated two-dimensional MnO$_2$

Two-dimensional (2D) materials are suitable hosts for the intercalation of extrinsic guest ions such as Li+, Na+ and K+ as the interlayer coupling is weak. This allows ion intercalation engineering of 2D materials, which may be a key to advancing technological applications in energy storage, neuromorphic electronics, and bioelectronics. However, ions that are extrinsic to the host materials possess challenges in fabrication of devices as there are extra steps of ion intercalation. This results in degradation of the long-term stability of the intercalated atomically thin structures. Here, we introduce large-area single-crystal ultra-thin layered MnO$_2$ via chemical vapor deposition, spontaneously intercalated by potassium ions during the synthesis. We studied the ultra-thin 2D K-MnO$_2$ in detail and showed that charge transport in these crystals is dominated by motion of hydrated potassium ions in the interlayer space. Moreover, K-MnO$_2$ crystals exhibit reversible layered-to-spinel phase transition accompanied by an optical contrast change based on the electrical and optical modulation of the potassium and the interlayer water concentration. We used the electric field driven ionic motion in K-MnO$_2$ based devices to demonstrate the memristive properties of two terminal devices. As a possible application we showed that K-MnO$_2$ memristors display synapse-like behavior such as short and long-term potentiation and depression as well as ionic coupling effects.

cond-mat.mtrl-sci↗

arXiv2021

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation

In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with an Euler-type equation inspired by the thermomechanical Cucker--Smale (TCS) model. We propose a novel drag force for the fluid-particle interaction reminiscent of Stokes' law. Whilst the macroscopic species is regarded as a self-organized background fluid that affects the kinetic species, the latter is assumed sparse and does not affect the macroscopic dynamics. We propose two hyperbolic scalings, in terms of a strong and weak relaxation regime of the internal variable towards the background population. Under each regime, we prove the rigorous hydrodynamic limit towards a coupled system composed of two Euler-type equations. Inertial effects of momentum and internal variable in the kinetic species disappear for strong relaxation, whereas a nontrivial dynamics for the internal variable appears for weak relaxation. Our analysis covers both the case of Lipschitz and weakly singular influence functions

math.AP↗

arXiv2020

Hamilton-Jacobi Deep Q-Learning for Deterministic Continuous-Time Systems with Lipschitz Continuous Controls

In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from applying the dynamic programming principle to continuous-time Q-functions. A novel semi-discrete version of the HJB equation is proposed to design a Q-learning algorithm that uses data collected in discrete time without discretizing or approximating the system dynamics. We identify the condition under which the Q-function estimated by this algorithm converges to the optimal Q-function. For practical implementation, we propose the Hamilton-Jacobi DQN, which extends the idea of deep Q-networks (DQN) to our continuous control setting. This approach does not require actor networks or numerical solutions to optimization problems for greedy actions since the HJB equation provides a simple characterization of optimal controls via ordinary differential equations. We empirically demonstrate the performance of our method through benchmark tasks and high-dimensional linear-quadratic problems.

cs.LG↗

arXiv2020

Hamilton-Jacobi-Bellman Equations for Maximum Entropy Optimal Control

Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a first step toward their extension to continuous-time systems, this paper considers continuous-time deterministic optimal control problems with entropy regularization. Applying the dynamic programming principle, we derive a novel class of Hamilton-Jacobi-Bellman (HJB) equations and prove that the optimal value function of the maximum entropy control problem corresponds to the unique viscosity solution of the HJB equation. Our maximum entropy formulation is shown to enhance the regularity of the viscosity solution and to be asymptotically consistent as the effect of entropy regularization diminishes. A salient feature of the HJB equations is computational tractability. Generalized Hopf-Lax formulas can be used to solve the HJB equations in a tractable grid-free manner without the need for numerically optimizing the Hamiltonian. We further show that the optimal control is uniquely characterized as Gaussian in the case of control affine systems and that, for linear-quadratic problems, the HJB equation is reduced to a Riccati equation, which can be used to obtain an explicit expression of the optimal control. Lastly, we discuss how to extend our results to continuous-time model-free RL by taking an adaptive dynamic programming approach. To our knowledge, the resulting algorithms are the first data-driven control methods that use an information theoretic exploration mechanism in continuous time.

math.OC↗

arXiv2020

Multi-Objective Predictive Taxi Dispatch via Network Flow Optimization

In this paper, we discuss a large-scale fleet management problem in a multi-objective setting. We aim to seek a receding horizon taxi dispatch solution that serves as many ride requests as possible while minimizing the cost of relocating vehicles. To obtain the desired solution, we first convert the multi-objective taxi dispatch problem into a network flow problem, which can be solved using the classical minimum cost maximum flow (MCMF) algorithm. We show that a solution obtained using the MCMF algorithm is integer-valued; thus, it does not require any additional rounding procedure that may introduce undesirable numerical errors. Furthermore, we prove the time-greedy property of the proposed solution, which justifies the use of receding horizon optimization. For computational efficiency, we propose a linear programming method to obtain an optimal solution in near real time. The results of our simulation studies using real-world data for the metropolitan area of Seoul, South Korea indicate that the performance of the proposed predictive method is almost as good as that of the oracle that foresees the future.

eess.SY↗

arXiv2020

Hamilton-Jacobi-Bellman Equations for Q-Learning in Continuous Time

In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the unique viscosity solution of the HJB equation. A necessary and sufficient condition for optimality is provided using the viscosity solution framework. By using the HJB equation, we develop a Q-learning method for continuous-time dynamical systems. A DQN-like algorithm is also proposed for high-dimensional state and control spaces. The performance of the proposed Q-learning algorithm is demonstrated using 1-, 10- and 20-dimensional dynamical systems.

math.OC↗

arXiv2019

Propagation of the mono-kinetic solution in the Cucker-Smale-type kinetic equations

In this paper, we study the propagation of the mono-kinetic distribution in the Cucker-Smale-type kinetic equations. More precisely, if the initial distribution is a Dirac mass for the variables other than the spatial variable, then we prove that this "mono-kinetic" structure propagates in time. For that, we first obtain the stability estimate of measure-valued solutions to the kinetic equation, by which we ensure the uniqueness of the mono-kinetic solution in the class of measure-valued solutions with compact supports. We then show that the mono-kinetic distribution is a special measure-valued solution. The uniqueness of the measure-valued solution implies the desired propagation of mono-kinetic structure.

math.AP↗

arXiv2019

A kinetic description for the herding behavior in financial market

As a continuation of the study of the herding model proposed in (Bae et al. in arXiv:1712.01085, 2017), we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the mean-field limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat's lemma. We, however, don't get any herding rate in this case. On the other hand, we also establish a Grönwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.

math.AP↗