arXiv subjects

Chenglong Xu

Publications and source records attributed to Chenglong Xu.

7 recordsLinked to original sources

arXiv2026

An hp-version time stepping spectral Monte Carlo method for semi-linear parabolic equations

In this paper, we present an $hp$-version time-stepping spectral Monte Carlo method for solving semi-linear parabolic equations. The key innovation lies in constructing an exponentially accurate stochastic algorithm that integrates a residual iteration scheme on Gauss-type nodes in both temporal and spatial directions with a reconstruction strategy rooted in spectral methods. To address the long-time simulations and initial singularities that are often challenging for traditional stochastic algorithms (e.g., walk-on-spheres method), we further develop an $hp$-version time-stepping framework that employs multiple time steps and, respectively, geometric time partitions with linearly increasing polynomial degrees to handle these difficulties. Notably, the proposed algorithm bypasses the need to solve linear systems required by traditional spectral methods and remarkably supports parallel computation at both temporal and spatial grid points. We rigorously establish exponential convergence rates for the multistep method within a finite number of iterations. Extensive numerical experiments are conducted to demonstrate the spectral accuracy and computational efficiency of the proposed method in long-time simulations, problems with initial singularities, and a five-dimensional problem, thereby validating the theoretical results.

math.NA↗

arXiv2026

TableVista: Benchmarking Multimodal Table Reasoning under Visual and Structural Complexity

We introduce TableVista, a comprehensive benchmark for evaluating foundation models in multimodal table reasoning under visual and structural complexity. TableVista consists of 3,000 high-quality table reasoning problems, where each instance is expanded into 10 distinct visual variants through our multi-style rendering and transformation pipeline. This process encompasses diverse scenario styles, robustness perturbations, and vision-only configurations, culminating in 30,000 multimodal samples for a multi-dimensional evaluation. We conduct an extensive evaluation of 29 state-of-the-art open-source and proprietary foundation models on TableVista. Through comprehensive quantitative and qualitative analysis, we find that while evaluated models remain largely stable across diverse rendering styles, they exhibit pronounced performance degradation on complex structural layouts and vision-only settings, revealing that current models struggle to maintain reasoning consistency when structural complexity combines with visually integrated presentations. These findings highlight critical gaps in current multimodal capabilities, providing insights for advancing more robust and reliable table understanding models.

cs.CL↗

arXiv2025

Efficient implicit-explicit sparse stochastic method for high dimensional semi-linear nonlocal diffusion equations

In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial integro-differential equations (PIDEs), in which the operator captures both local convection-diffusion and nonlocal diffusion effects, as revealed by its limiting behavior with respect to the interaction radius. To overcome the bottleneck of computational complexity caused by the curse of dimensionality and the dense linear systems arising from nonlocal operators, we propose a novel implicit-explicit scheme based on a direct approximation of the nonlinear Feynman-Kac representation. The incorporation of sparse grid interpolation significantly enhances the algorithm's scalability and enables its application to problems in high dimensions. To further address the challenges posed by hypersingular kernels, we design a sampling strategy tailored to their singular structure, which ensures accurate and stable treatment of the nonlocal operators within the probabilistic framework. Notably, the proposed method inherits unconditional stability from the underlying stochastic representation, without imposing constraints on the temporal and spatial discretization scales. A rigorous error analysis is provided to establish the convergence of the proposed scheme. Extensive numerical experiments, including some non-radial solutions in up to 100 dimensions, are presented to validate the robustness and accuracy of the proposed method.

math.NA↗

arXiv2025

Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates

This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by $\alpha$-stable L\'evy process with $\alpha\in (0,2)$, which was initially proposed and developed by Gobet and Maire in their pioneering works (Monte Carlo Methods Appl 10(3-4), 275--285, 2004, and SIAM J Numer Anal 43(3), 1256--1275, 2005) for the case $\alpha=2$. The novel method effectively integrates multiple computational techniques, including the interpolation based on generalized Jacobi functions (GJFs), space-time spectral methods, control variates techniques, and a novel walk-on-sphere method (WOS). The exponential convergence of the error bounds is rigorously established through finite iterations for both Poisson and parabolic equations involving the integral fractional Laplacian operator. Remarkably, the proposed space-time spectral Monte Carlo method (ST-SMC) for the parabolic equation is unified for both $\alpha\in(0,2)$ and $\alpha=2$. Extensive numerical results are provided to demonstrate the spectral accuracy and efficiency of the proposed method, thereby validating the theoretical findings.

math.NA↗

arXiv2024

Esports Debut as a Medal Event at 2023 Asian Games: Exploring Public Perceptions with BERTopic and GPT-4 Topic Fine-Tuning

This study examined the public opinions of esports at the 2023 Asian Games and value co-creation during the event using an LLM-enhanced BERTopic modeling analysis. We identified five major themes representing public perceptions, as well as how major stakeholders co-created value within and beyond the esports ecosystem. Key findings highlighted the strategic use of social media marketing to influence public opinion and promote esports events and brands, emphasizing the importance of event logistics and infrastructure. Additionally, the study revealed the co-creation value contributed by stakeholders outside the traditional esports ecosystem, particularly in promoting national representation and performance. Our findings supported the ongoing efforts to legitimize esports as a sport, noting that mainstream recognition remains a challenge. The inclusion of esports as a medal event showcased broader acceptance and helped mitigate negative public perceptions. Moreover, contributions from non-traditional stakeholders underscored the value of cross-subcultural collaborations in esports.

cs.HC↗

arXiv2023

Intrinsic defect engineering of CVD grown monolayer MoS$_2$ for tuneable functional nanodevices

Defects in atomically thin materials can drive new functionalities and expand applications to multifunctional systems that are monolithically integrated. An ability to control formation of defects during the synthesis process is an important capability to create practical deployment opportunities. Molybdenum disulfide (MoS$_2$), a two-dimensional (2D) semiconducting material harbors intrinsic defects that can be harnessed to achieve tuneable electronic, optoelectronic, and electrochemical devices. However, achieving precise control over defect formation within monolayer MoS$_2$, while maintaining the structural integrity of the crystals remains a notable challenge. Here, we present a one-step, in-situ defect engineering approach for monolayer MoS$_2$ using a pressure dependent chemical vapour deposition (CVD) process. Monolayer MoS$_2$ grown in low-pressure CVD conditions (LP-MoS$_2$) produces sulfur vacancy (Vs) induced defect rich crystals primarily attributed to the kinetics of the growth conditions. Conversely, atmospheric pressure CVD grown MoS$_2$ (AP-MoS$_2$) passivates these Vs defects with oxygen. This disparity in defect profiles profoundly impacts crucial functional properties and device performance. AP-MoS$_2$ shows a drastically enhanced photoluminescence, which is significantly quenched in LP-MoS$_2$ attributed to in-gap electron donor states induced by the Vs defects. However, the n-doping induced by the Vs defects in LP-MoS$_2$ generates enhanced photoresponsivity and detectivity in our fabricated photodetectors compared to the AP-MoS$_2$ based devices. Defect-rich LP-MoS$_2$ outperforms AP-MoS$_2$ as channel layers of field-effect transistors (FETs), as well as electrocatalytic material for hydrogen evolution reaction (HER). This work presents a single-step CVD approach for in-situ defect engineering in monolayer MoS$_2$ and presents a pathway to control defects in other monolayer material systems.

physics.app-ph↗

arXiv2022

Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions

In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac representation based on the Green function for the fractional Laplacian operator on the unit ball in arbitrary dimensions. Inspired by the "walk-on-spheres" algorithm proposed in [24], we extend our algorithm for solving fractional PDEs in the complex domain. Then, we can compute the expectation of a multi-dimensional random variable with a known density function to obtain the numerical solution efficiently. The proposed algorithm finds it remarkably efficient in solving fractional PDEs: it only needs to evaluate the integrals of expectation form over a series of inside ball tangent boundaries with the known Green function. Moreover, we carry out the error estimates of the proposed method for the $n$-dimensional unit ball. Finally, ample numerical results are presented to demonstrate the robustness and effectiveness of this approach for fractional PDEs in unit disk and complex domains, and even in ten-dimensional unit balls.

math.NA↗