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Weiren Zhao

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Published work

8 published item(s)

preprint2026arXiv

SynerMedGen: Synergizing Medical Multimodal Understanding with Generation via Task Alignment

Unifying multimodal understanding and generation is a compelling frontier that is beginning to emerge in the medical field. However, the limited existing unified medical models typically treat understanding and generation as disjoint objectives, lacking a meaningful functional synergy. In this work, we identify and address a critical question in unified medical modeling: what form of understanding truly benefits generation. We present SynerMedGen, a unified framework built on the proposed principle of generation-aligned understanding, which synergizes understanding objectives with generation tasks via task alignment. SynerMedGen introduces three generation-aligned understanding tasks and a two-stage training strategy that transfers generation-beneficial representations learned during understanding training to medical image synthesis. Remarkably, even with understanding training alone, our SynerMedGen achieves strong zero-shot performance across 22 medical image synthesis tasks and demonstrates robust generalization to unseen datasets. When combined with generation training, SynerMedGen consistently outperforms state-of-the-art specialized medical image synthesis models as well as recent unified medical models. We also release a large-scale dataset named SynerMed consisting of 1M paired synthesis samples and 2M generation-derived understanding instances to support further research on understanding-generation synergy. Our project can be accessed at https://github.com/Mhilab/SynerMedGen.

preprint2022arXiv

Asymptotic stability for two-dimensional Boussinesq systems around the Couette flow in a finite channel

In this paper, we study the asymptotic stability for the two-dimensional Navier-Stokes Boussinesq system around the Couette flow with small viscosity $ν$ and small thermal diffusion $μ$ in a finite channel. In particular, we prove that if the initial velocity and initial temperature $(v_{in},ρ_{in})$ satisfies $\|v_{in}-(y,0)\|_{H_{x,y}^2}\leq \e_0 \min\{ν,μ\}^{\f12}$ and $\|ρ_{in}-1\|_{H_x^{1}L_y^2}\leq \e_1 \min\{ν,μ\}^{\f{11}{12}}$ for some small $\e_0,\e_1$ independent of $ν, μ$, then for the solution of the two-dimensional Navier-Stokes Boussinesq system, the velocity remains within $O(\min\{ν,μ\}^{\f12})$ of the Couette flow, and approaches to Couette flow as $t\to\infty$; the temperature remains within $O(\min\{ν,μ\}^{\f{11}{12}})$ of the constant $1$, and approaches to $1$ as $t\to\infty$.

preprint2022arXiv

Asymptotic stability of two-dimensional Couette flow in a viscous fluid

In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $ν>0$ in $\mathbb{T}\times\mathbb{R}$. It's generally known the nonlinear asymptotic stability of the Couette flow depends closely on the size and regularity of the initial perturbation, which yields the stability threshold problem. This work studies the relationship between the size and the regularity of the initial perturbation that makes the nonlinear asymptotic stability holds. More precisely, we proved that if the initial perturbation is in some Gevrey-$\frac{1}{s}$ class with size $εν^β$ where $s\geq \frac{1-3β}{2-3β}$ and $β\in [0,\frac{1}{3}]$, then the nonlinear asymptotic stability holds.

preprint2022arXiv

Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number $γ^2>\frac{1}{4}$

In this paper, we study the nonlinear asymptotic stability of the Couette flow in the stably stratified regime, namely the Richardson number $γ^2>\frac{1}{4}$. Precisely, we prove that if the initial perturbation $(u_{in},\vartheta_{in})$ of the Couette flow $v_s=(y,0)$ and the linear temperature $ρ_s=-γ^2y+1$ satisfies $\|u_{in}\|_{H^{s+1}}+\|\vartheta_{in}\|_{H^{s+2}}\leq ε_0ν^{\frac{1}{2}}$, then the asymptotic stability holds.

preprint2019arXiv

Stability threshold of the 2D Couette flow in Sobolev spaces

We study the stability threshold of the 2D Couette flow in Sobolev spaces at high Reynolds number $Re$. We prove that if the initial vorticity $Ω_{in}$ satisfies $\|Ω_{in}-(-1)\|_{H^σ}\leq εRe^{-1/3}$, then the solution of the 2D Navier-Stokes equation approaches to some shear flow which is also close to Couette flow for time $t\gg Re^{1/3}$ by a mixing-enhanced dissipation effect and then converges back to Couette flow when $t\to +\infty$.

preprint2015arXiv

Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary

In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschtiz function and the free surface belongs to $C^{\f32+\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.