arXiv subjects

Xinhua Li

Publications and source records attributed to Xinhua Li.

6 recordsLinked to original sources

arXiv2026

Smoothness of Inertial Manifold for the Burgers Equation

This paper establishes a ${C^{n,\varepsilon }}$-smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior can be completely determined by explicit smooth first-order ODEs. We first devise a new framework for an abstract equation with two nonlinear terms, where one preserves regularity and the other reduces regularity, and derive sufficient conditions for constructing the ${C^{n,\varepsilon}}$-smooth extension of the IM by treating these two nonlinear terms separately.

math.DS↗

arXiv2026

DeepFWI: Identifying Bug-Sensitive Warnings with Multi-Modal Code-Warning Semantics

Static analysis tools have evolved over time to assist in detecting bugs. However, the excessive false warnings can impede developers' productivity and confidence in the tools. Previous research efforts have explored learning-based approaches to identify bug warnings. Nevertheless, their coarse granularity, focusing on either long-term warnings or function-level alerts, is insensitive to individual bugs. Also, they rely on manually crafted features or solely on source code semantics, which is inadequate for effective learning. In this paper, we propose DeepFWI, a learning-based approach that identifies bug-sensitive warnings at a fine-grained granularity. Specifically, we design a novel LSTM-based model that captures multi-modal semantics of source code and warnings from automated static analysis tools (ASATs) and highlights their correlations with cross-attention. To tackle the data scarcity of training and evaluation, we collected a large-scale dataset of 280,273 warnings. We conducted extensive experiments on the dataset to evaluate DeepFWI. The experimental results demonstrate the effectiveness of our approach, with an F1-score 67.06% for confirming true warnings in a finer-grained manner, significantly outperforming all baselines. Additionally, to validate the practicality of DeepFWI from the perspective of developers, we applied DeepFWI to four popular open-source projects. Our approach filtered out the vast majority of warnings, while still successfully surfacing 25 true bug-related warnings that were confirmed through manual analysis.

cs.SE↗

arXiv2025

Modeling Variants of Prompts for Vision-Language Models

Large pre-trained vision-language models (VLMs) offer a promising approach to leveraging human language for enhancing downstream tasks. However, VLMs such as CLIP face significant limitation: its performance is highly sensitive to prompt template design. Although prompt learning methods can address the sensitivity issue by replacing natural language prompts with learnable ones, they are incomprehensible to humans. Ensuring consistent performance across various prompt templates enables models to adapt seamlessly to diverse phrasings, enhancing their ability to handle downstream tasks without requiring extensive prompt engineering. In this work, we introduce the RobustPrompt Benchmark, a systematic benchmark to evaluate robustness to different prompt templates for VLMs. It includes a dataset with hundreds of carefully designed prompt templates, divided into six types, covering a wide variety of commonly used templates. Beside the benchmark, we propose Modeling Variants of Prompts (MVP), a simple yet effective method that mitigates sensitivity by modeling variants of prompt structures. The innovation of MVP lies in decoupling prompts into templates and class names, and using Variational Autoencoders (VAE) to model the distribution of diverse prompt structures. Experiments across 11 datasets demonstrate that MVP can greatly enhance model robustness to variations in input prompts without a drop in performance. The code is available at https://github.com/liaolea/MVP.

cs.CV↗

arXiv2020

Experimental and numerical studies on kV scattered x-ray imaging for real-time image guidance in radiation therapy

Motion management is a critical component of image guidance radiotherapy for lung cancer. We previously proposed a scheme using kV scattered x-ray photons for marker-less real-time image guidance in lung cancer radiotherapy. This study reports our recently progress using the photon counting detection technique to demonstrate potential feasibility of this method and using Monte Carlo (MC) simulations and ray-tracing calculations to characterize the performance. In our scheme, a thin slice of x-ray beam was directed to the target and we measured the outgoing scattered photons using a photon counting detector with a parallel-hole collimator to establish the correspondence between detector pixels and scatter positions. Image corrections of geometry, beam attenuation and scattering angle were performed to convert the raw image to the actual image of Compton attenuation coefficient. We set up a MC simulation system using an in-house developed GPU-based MC package modeling the image formation process. We also performed ray-tracing calculations to investigate the impacts of imaging system geometry on resulting image resolution. The experiment demonstrated feasibility of using a photon counting detector to measure scattered x-ray photons and generate the proposed scattered x-ray image. After correction, x-ray scattering image intensity and Compton scattering attenuation coefficient were linearly related, with R2=0.91. Contrast to Noise Ratios of different objects were improved and the values in experimental results and MC simulation results agreed with each other. Ray-tracing calculations revealed the dependence of image resolution on imaging geometry. The image resolution increases with reduced source to object distance and increased collimator height. The study demonstrated potential feasibility of using scattered x-ray imaging as a real-time image guidance method in radiation therapy.

physics.med-ph↗

arXiv2020

Inertial manifolds via spatial averaging revisited

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn-Hilliard equations, including fractional and 6th order Cahn-Hilliard equations and several classes of modified Navier-Stokes equations including the Leray-$α$ regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.

math.AP↗

arXiv2019

Inertial manifolds for the incompressible Navier-Stokes equations

In this article, we devote to the existence of an $N$-dimensional inertial manifold for the incompressible Navier-Stokes equations in $\mathbb{T}^{d}$ ($d=2,3$). Our results can be summarized as two aspects: Firstly, we construct an $N$-dimensional inertial manifold for the Navier-Stokes equations in $\mathbb{T}^{2}$; Secondly, we extend slightly the spatial averaging method to the abstract case: $\partial_{t}u+A^{1+α}u+A^αF(u)=f$ (here $0<α<1$, $A>0$ is a self-adjoint operator with compact inverse and $F$ is Lipschitz from a Hilbert space $\mathbb{H}$ to $\mathbb{H}$), and then verify the existence of an $N$-dimensional inertial manifold for the hyperviscous Navier-Stokes equation with the hyperviscous index $5/4$ in $\mathbb{T}^{3}$.

math.AP↗