arXiv subjects

Zhaoyang Shang

Publications and source records attributed to Zhaoyang Shang.

5 recordsLinked to original sources

arXiv2025

Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients

It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations with temperature-dependent coefficients in the whole space. When the initial density and the initial temperature are linearly equivalent to some large constant states, we establish the first result on the global existence of large strong solution. Moreover, the optimal decay rates of the solution to its associated equilibrium are established when the initial data belong to $L^{p_0}(\mathbb{R}^3)$ for some $p_0\in[1,2]$.

math.AP↗

arXiv2025

A benchmark dataset for evaluating Syndrome Differentiation and Treatment in large language models

The emergence of Large Language Models (LLMs) within the Traditional Chinese Medicine (TCM) domain presents an urgent need to assess their clinical application capabilities. However, such evaluations are challenged by the individualized, holistic, and diverse nature of TCM's "Syndrome Differentiation and Treatment" (SDT). Existing benchmarks are confined to knowledge-based question-answering or the accuracy of syndrome differentiation, often neglecting assessment of treatment decision-making. Here, we propose a comprehensive, clinical case-based benchmark spearheaded by TCM experts, and a specialized reward model employed to quantify prescription-syndrome congruence. Data annotation follows a rigorous pipeline. This benchmark, designated TCM-BEST4SDT, encompasses four tasks, including TCM Basic Knowledge, Medical Ethics, LLM Content Safety, and SDT. The evaluation framework integrates three mechanisms, namely selected-response evaluation, judge model evaluation, and reward model evaluation. The effectiveness of TCM-BEST4SDT was corroborated through experiments on 15 mainstream LLMs, spanning both general and TCM domains. To foster the development of intelligent TCM research, TCM-BEST4SDT is now publicly available.

cs.CL↗

arXiv2025

The Harder The Better: Maintaining Supervised Fine-tuning Generalization with Less but Harder Data

Large Language Models (LLMs) excel in general tasks, but adapting them to specialized domains relies on high-quality supervised fine-tuning (SFT) data. Although existing methods can identify subsets of high-quality data and reduce training cost to some extent, their selection process still suffers from over-reliance on LLMs' internal knowledge, weak interpretability, and limited generalization. To address these limitations, we propose THTB (The Harder The Better), a cognitive science-inspired framework for instruction data selection and annotation guidance. THTB prioritizes higher-level cognitive instructions by combining quality filtering with intrinsic and extrinsic hardness scoring, offering interpretable and quantifiable criteria for efficient SFT, both in data selection and annotation guidance. Experiments show that THTB enables models trained on only 5% of the data to outperform full-dataset training, while achieving superior generalization compared with LLM-only selection. In addition, THTB provides effective annotation guidance in vertical domains, enabling a model trained on just 2% of the data to surpass models trained on much larger datasets, demonstrating strong potential for domain adaptation. Our code, datasets, and models are available on https://github.com/DYJG-research/THTB.

cs.CL↗

arXiv2024

Global Existence and Asymptotic Behavior of Large Strong Solutions to the 3D Full Compressible Navier-Stokes Equations with Density-dependent Viscosities

The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity is considered. By introducing the modified effective viscous flux and using the bootstrap argument, we establish the global existence of large strong solution when the initial density is linearly equivalent to a large constant state. It is worthy of mentioning that, different from the work of Matsumura and Nishida (J. Math. Kyoto Univ., 1980) with small initial perturbation and the work of Huang and Li (Arch. Ration. Mech. Anal., 2018) with small energy but possibly large oscillations, our global large strong solution is uniform-in-time in $H^2$ Sobolev space and the uniform-in-time bounds of both density and temperature are obtained without any restrictions on the size of initial velocity and initial temperature. In addition, when the initial data belongs to $L^{p_0}\cap H^2$ with $p_0\in[1,2]$, we establish the convergence of the solution to its associated equilibrium with an explicit decay rate whether the initial data close to or far away from the equilibrium in the whole space. As a result, we give a specific large strong solution in Sobolev space satisfying the global existence assumptions proposed by Villani (Mem. Amer. Math. Soc., 2009), He, Huang, and Wang (Arch. Ration. Mech. Anal., 2019), Zhang and Zi (Ann. Inst. H. Poincare Anal. Non Lineaire, 2020) in studying the asymptotic behavior of solution, and extend the second above result to the nonisentropic case. This paper considers for the first time the application of Fourier splitting method to Navier-Stokes equations with variable viscosity.

math.AP↗

arXiv2024

Global Strong Solutions to the Cauchy Problem of Three-dimensional Isentropic Magnetohydrodynamics Equations with Large Initial Data

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that strong solutions exist globally in time, and there is no restriction on the size of the initial velocity and initial magnetic field.

math.AP↗