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Junha Kim

Publications and source records attributed to Junha Kim.

At least 19 recordsLinked to original sources
arXiv2026

Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium

This paper studies the Cauchy problem for the fully parabolic Keller-Segel system. The main results show that there exists a critical threshold $A_{\rm crit}>0$ for steady states $(A,A)$ such that the steady states are nonlinearly stable when $A\le A_{\rm crit}$ and nonlinearly unstable when $A>A_{\rm crit}$. We discuss asymptotic convergence rates as well. In the subcritical case $A<A_{\rm crit}$, the rates correspond to those of the heat equation, and in the critical case $A=A_{\rm crit}$, the rates correspond to half those of the heat equation.

math.AP↗
arXiv2026

High-Resolution Artwork Outpainting with Global Blueprint Guidance and Layout Control

Image outpainting extends an image beyond its original borders, requiring seamless style integration and globally coherent scene completion. Building on the success of diffusion models, recent methods have achieved substantial improvements in visual quality. In practice, however, high-resolution outpainting is commonly performed via progressive expansion around a fixed source image, particularly in artwork scenarios. Despite this progress, existing approaches still suffer from three key limitations: (i) the absence of a reliable global planning mechanism, which leads to structural instability and error accumulation at high resolutions; (ii) limited spatial controllability beyond text prompts, making it difficult to place objects at user-specified locations; and (iii) high inference latency caused by inherently sequential patch generation. To address these issues, we propose a global blueprint-guided two-stage diffusion framework for layout-controllable high-resolution outpainting with efficient parallel synthesis. In Stage 1, we generate a low-resolution global blueprint using a layout adapter that injects bounding-box conditions into a Stable Diffusion inpainting backbone, producing a globally consistent structural plan while extracting global guidance features. In Stage 2, we synthesize high-resolution local patches in parallel by injecting the blueprint-derived global guidance and initializing each patch from the blueprint using the low-frequency preservation property of forward diffusion. This design eliminates sequential dependency while maintaining global coherence. Extensive experiments on large-scale artwork datasets demonstrate improved visual fidelity, stronger semantic consistency, and substantially reduced inference time compared to prior baselines, while uniquely supporting explicit layout control for artwork outpainting.

cs.CV↗
arXiv2026

CHIA: An open-source framework for principled, agentic AI-driven hardware/software co-design research

Agentic artificial intelligence shows great promise for radically improving the pace of innovation in hardware/software co-design research across computer architecture, systems, compilers, and VLSI. Thus far, however, applications of AI in these contexts have generally been demonstrated in isolated settings on small-scale problems, due to the difficulty of designing and deploying complex AI-infused hardware and software development workflows. This paper introduces CHIA, an open-source hardware/software co-design framework for agile and principled research on the application of AI to co-design. CHIA treats the productive construction and scalable deployment of the co-design flow itself as a first-class objective. In CHIA, agentic AI-driven hardware and software design flows are expressed as CHIA loops: directed cyclic graphs whose nodes execute various system-on-chip design tools, microarchitectural simulators, software build systems, AI models, evolutionary coding agents, and more. The CHIA library provides node implementations for many popular tools, including Chipyard, gem5, ChampSim, FireSim, Hammer (thus several commercial ASIC CAD tools), Vivado, AlphaEvolve, AdaEvolve, and many others. CHIA also provides a broad set of features to conduct principled science around these flows. These include isolation between AI models and hardware tools, profiling mechanisms, fault-tolerant execution, and reliability at scale across hundreds of heterogeneous systems (CPUs, FPGAs, GPUs, etc., across public cloud/on-prem.). To showcase CHIA, we present five CHIA loops as case studies: (1) automatic RTL-to-gem5 simulator alignment, (2) LLM-driven implementation of microarchitectural features in RTL, (3) agentic, IPC-aware critical path optimization, (4) evolutionary architectural discovery, and (5) maintainer-friendly agentic GitHub issue fixing.

cs.AR↗
arXiv2025

Asymptotic stability of the $2D$ temperature-dependent tropical climate model with the sharp decay rates

We investigate the asymptotic stability of a tropical climate model posed on $\bR^2$, with temperature-dependent diffusion in the barotropic mode $u$ and linear damping in the first baroclinic mode $v$. We consider two distinct cases for the barotropic component: one with linear damping and one without. For both cases, we prove the small data global existence of smooth solutions. Furthermore, we establish sharp temporal decay estimates for solutions in arbitrary Sobolev norms $H^m (\bR^2)$, $m \ge 0$.

math.AP↗
arXiv2025

Wellposedness of inviscid SQG in the half-plane

We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3,p}$ and $C^{2,\beta}$ for any $1<p<\infty$ and $0<\beta<1$. We complement this wellposedness by showing that for generic $C^{\infty}_{0}$ initial data, the unique corresponding solution does not belong to $W^{3,\infty}$.

math.AP↗
arXiv2025

Convergence and non-convergence phenomena in Euler-Maxwell to MHD transitions

In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD system, auxiliary linear system and error part system. As a result, we obtain the convergence of the velocity of the fluid $u$, electric fields $E$ and magnetic fields $B$ from the Euler-Maxwell system toward the MHD system in $L^{p}_{t}L^{2}_{x}$ as the speed of light $c$ approaches infinity for $p\in[1,\infty]$. We also derived non-convergence results of electric current $j$ or $cE$, and these results are classified by a certain threshold for $p$. Finally, we investigate how the $L^2$-energy flow of Euler-Maxwell system evolves as c tends to infinity, leading to the vanishing of Amp\`ere's equation in the Euler-Maxwell system.

math.AP↗
arXiv2025

On the axially symmetric solutions to the spatially homogeneous Landau equation

In this paper, we consider the spatially homogeneous Landau equation, which is a variation of the Boltzmann equation in the grazing collision limit. For the Landau equation for hard potentials in the style of Desvillettes-Villani (Comm. Partial Differential Equations, 2000), we provide the proof of the existence of axisymmetric measure-valued solution for any axisymmetric $\mathcal{P}_p(\mathbb{R}^3)$ initial profile for any $p\ge 2$. Moreover, we prove that if the initial data is not a single Dirac mass, then the solution instantaneously becomes analytic for any time $t>0$ in the hard potential case. In the soft potential and the Maxwellian molecule cases, we show that there are no solutions whose support is contained in a fixed line even for any given line-concentrated data.

math.AP↗
arXiv2024

Is user feedback always informative? Retrieval Latent Defending for Semi-Supervised Domain Adaptation without Source Data

This paper aims to adapt the source model to the target environment, leveraging small user feedback (i.e., labeled target data) readily available in real-world applications. We find that existing semi-supervised domain adaptation (SemiSDA) methods often suffer from poorly improved adaptation performance when directly utilizing such feedback data, as shown in Figure 1. We analyze this phenomenon via a novel concept called Negatively Biased Feedback (NBF), which stems from the observation that user feedback is more likely for data points where the model produces incorrect predictions. To leverage this feedback while avoiding the issue, we propose a scalable adapting approach, Retrieval Latent Defending. This approach helps existing SemiSDA methods to adapt the model with a balanced supervised signal by utilizing latent defending samples throughout the adaptation process. We demonstrate the problem caused by NBF and the efficacy of our approach across various benchmarks, including image classification, semantic segmentation, and a real-world medical imaging application. Our extensive experiments reveal that integrating our approach with multiple state-of-the-art SemiSDA methods leads to significant performance improvements.

cs.CV↗
arXiv2024

On well/ill-posedness for the generalized surface quasi-geostrophic equations in H\"older spaces

We establish the well/ill-posedness theories for the inviscid $\alpha$-surface quasi-geostrophic ($\alpha$-SQG) equations in H\"older spaces, where $\alpha = 0$ and $\alpha = 1$ correspond to the two-dimensional Euler equation in the vorticity formulation and SQG equation of geophysical significance, respectively. We first prove the local-in-time well-posedness of $\alpha$-SQG equations in $C([0,T);C^{0,\beta}(\mathbb{R}^2))$ with $\beta \in (\alpha,1)$ for some $T>0$. We then analyze the strong ill-posedness in $C^{0,\alpha}(\mathbb{R}^2)$ constructing smooth solutions to the $\alpha$-SQG equations that exhibit $C^{0,\alpha}$--norm growth in a short time. In particular, we develop the nonexistence theory for $\alpha$-SQG equations in $C^{0,\alpha}(\mathbb{R}^2)$.

math.AP↗
arXiv2023

On well-posedness of $α$-SQG equations in the half-plane

We investigate the well-posedness of $α$-SQG equations in the half-plane, where $α=0$ and $α=1$ correspond to the 2D Euler and SQG equations respectively. For $0<α\le 1/2$, we prove local well-posedness in certain weighted anisotropic Hölder spaces. We also show that such a well-posedness result is sharp: for any $0<α\le 1$, we prove nonexistence of Hölder regular solutions (with the Hölder regularity depending on $α$) for initial data smooth up to the boundary.

math.AP↗
arXiv2023

Enhancing Breast Cancer Risk Prediction by Incorporating Prior Images

Recently, deep learning models have shown the potential to predict breast cancer risk and enable targeted screening strategies, but current models do not consider the change in the breast over time. In this paper, we present a new method, PRIME+, for breast cancer risk prediction that leverages prior mammograms using a transformer decoder, outperforming a state-of-the-art risk prediction method that only uses mammograms from a single time point. We validate our approach on a dataset with 16,113 exams and further demonstrate that it effectively captures patterns of changes from prior mammograms, such as changes in breast density, resulting in improved short-term and long-term breast cancer risk prediction. Experimental results show that our model achieves a statistically significant improvement in performance over the state-of-the-art based model, with a C-index increase from 0.68 to 0.73 (p < 0.05) on held-out test sets.

cs.CV↗
arXiv2022

Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain

We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.

math.AP↗
arXiv2022

Quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation on the three fundamental domains

We analyze the asymptotic stability of the quasi-linearly stratified densities in the 2D inviscid incompressible porous medium equation on $\bbR^2$ with respect to the buoyancy frequency $N$. Our target density of stratification is the sum of the large background linear profile with its slope $N$ and the small perturbation that could be both non-linear and non-monotone. Quantification in $N$ will be performed not only on how large the initial density disturbance is allowed to be but also on how much the target densities can deviate from the purely linear density stratification without losing their stability. For the purely linear density stratification, our method robustly applies to the three fundamental domains $\bbR^2,$ $\bbT^2,$ and $\bbT\times[-1,1]$, improving both the previous result by Elgindi (On the asymptotic stability of stationary solutions of the inviscid incompressible porous medium equation, Archive for Rational Mechanics and Analysis, 225(2), 573-599, 2017) on $\bbR^2$ and $\bbT^2$, and the study by Castro-C\'ordoba-Lear (Global existence of quasi-stratified solutions for the confined IPM equation. Archive for Rational Mechanics and Analysis, 232(1), 437-471, 2019) on $\bbT\times[-1,1]$. The obtained temporal decay rates to the stratified density on $\bbR^2$ and to the newly found asymptotic density profiles on $\bbT^2$ and $\bbT\times[-1,1]$ are all sharp, fully realizing the level of the linearized system. We require the initial disturbance to be small in $H^m$ for any integer $m\geq 4$, which we even relax to any positive number $m>3$ via a suitable anisotropic commutator estimate.

math.AP↗
arXiv2022

Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator

We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively leveraging the anisotropy of the linear propagator that encodes both the partially dissipative nature of the non-resistive MHD system and the stabilizing mechanism of the underlying magnetic field. Isolating new key quantities and estimating them with themselves in an entangling way via the eigenvalue analysis based on Duhamel's formulation, we establish the global well-posedness for any initial data $(v_0,B_0)$ that is sufficiently small in a space rougher than $H^{4}\cap L^1$. This improves the recent work in SIAM J. Math. Anal. 47, 2630-2656 (2015) where the similar result was obtained provided that $(v_0,B_0)$ was small enough in a space strictly embedded in $H^{20}\cap W^{6,1}$.

math.AP↗
arXiv2022

Non-convergence of the rotating stratified flows toward the quasi-geostrophic dynamics

The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximation when the rotation-stratification ratio is either fixed to be unity or tends to unity sufficiently slowly in the asymptotic regime: the difference between the rotating stratified Boussinesq flow and the corresponding QG flow remains strictly away from zero, independently of the intensities of rotation and stratification. In contrast, we also show that the convergence occurs when the rotation-stratification ratio is fixed to be a number other than unity or converges to unity sufficiently fast. As a corollary, we compute a lower bound of the convergence rate, which blows up as the rotation-stratification ratio goes to unity.

math.AP↗
arXiv2022

Learning to Adapt to Unseen Abnormal Activities under Weak Supervision

We present a meta-learning framework for weakly supervised anomaly detection in videos, where the detector learns to adapt to unseen types of abnormal activities effectively when only video-level annotations of binary labels are available. Our work is motivated by the fact that existing methods suffer from poor generalization to diverse unseen examples. We claim that an anomaly detector equipped with a meta-learning scheme alleviates the limitation by leading the model to an initialization point for better optimization. We evaluate the performance of our framework on two challenging datasets, UCF-Crime and ShanghaiTech. The experimental results demonstrate that our algorithm boosts the capability to localize unseen abnormal events in a weakly supervised setting. Besides the technical contributions, we perform the annotation of missing labels in the UCF-Crime dataset and make our task evaluated effectively.

cs.CV↗