arXiv subjects

Jinwei Fang

Publications and source records attributed to Jinwei Fang.

5 recordsLinked to original sources

arXiv2026

Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data

We develop a rigorous numerical analysis framework for a class of semilinear parabolic problems with nonsmooth initial data. We employ a linear Galerkin finite element method for spatial discretization coupled with a high-order explicit exponential Runge-Kutta (EERK) temporal integration scheme. In contrast to conventional smooth error analysis, the nonsmooth case lacks a priori estimates for the higher-order derivatives of both the nonlinear term and the exact solution. By combining analytic semigroup techniques with fractional power space theory, we establish rigorous bounds for these derivatives. Finally, our analysis proves that the $p$th-order EERK method achieves a convergence rate of $\min(1 + \gamma/2 + \rho_1(\gamma)/2,\:p)$, where $\gamma$ characterizes the initial data regularity and $\rho_1(\gamma)$ quantifies the boundedness of the nonlinearity's first Fr\'echet derivative. Numerical experiments confirm the sharpness of these estimates.

math.NA↗

arXiv2026

GCA-BULF: A Bottom-Up Framework for Short-Term Load Forecasting Using Grouped Critical Appliances

With the rise of time-of-use and tiered electricity pricing, energy consumers are encouraged to adopt peak-shifting strategies by automatically controlling high-power appliances. These help lower energy costs while enhancing the power grid's stability. To support such energy management with high resilience and responsiveness, reliable short-term load forecasting (STLF) plays a critical role. STLF predicts electricity consumption over time horizons ranging from minutes to days, using historical data, temporal patterns, and contextual factors. Traditional top-down forecasting methods struggle to capture the complex consumption patterns of diverse and mixed appliance loads. Although bottom-up methods improve forecasting accuracy by integrating appliance-level data, monitoring all appliances is costly, and many do not meaningfully impact total load prediction. Therefore, we propose GCA-BULF, a bottom-up short-term load forecasting framework based on grouped critical appliances, supported by three key designs. First, the Critical Appliance Filtering module ranks appliances according to their power consumption, switching frequency, and usage pattern periodicity, and identifies critical ones through iterative load decomposition. Next, the Related Appliance Grouping module clusters these appliances based on spatial and temporal correlations for group-level forecasting. Finally, the Collaborative Load Forecasting module refines the total load prediction by combining multiple group-level forecasts. We evaluate GCA-BULF on residential and office building load forecasting tasks. Experimental results reveal that GCA-BULF improves hourly total load forecasting by 20.85%-57.88% compared to existing top-down methods and by 33.03%-92.48% compared to bottom-up methods.

cs.LG↗

arXiv2025

Exponential Runge-Kutta Galerkin finite element method for a reaction-diffusion system with nonsmooth initial data

This study presents a numerical analysis of the Field-Noyes reaction-diffusion model with nonsmooth initial data, employing a linear Galerkin finite element method for spatial discretization and a second-order exponential Runge-Kutta scheme for temporal integration. The initial data are assumed to reside in the fractional Sobolev space H^gamma with 0 < gamma < 2, where classical regularity conditions are violated, necessitating specialized error analysis. By integrating semigroup techniques and fractional Sobolev space theory, sharp fully discrete error estimates are derived in both L2 and H1 norms. This demonstrates that the convergence order adapts to the smoothness of initial data, a key advancement over traditional approaches that assume higher regularity. Numerical examples are provided to support the theoretical analysis.

math.NA↗

arXiv2025

IMDPrompter: Adapting SAM to Image Manipulation Detection by Cross-View Automated Prompt Learning

Using extensive training data from SA-1B, the Segment Anything Model (SAM) has demonstrated exceptional generalization and zero-shot capabilities, attracting widespread attention in areas such as medical image segmentation and remote sensing image segmentation. However, its performance in the field of image manipulation detection remains largely unexplored and unconfirmed. There are two main challenges in applying SAM to image manipulation detection: a) reliance on manual prompts, and b) the difficulty of single-view information in supporting cross-dataset generalization. To address these challenges, we develops a cross-view prompt learning paradigm called IMDPrompter based on SAM. Benefiting from the design of automated prompts, IMDPrompter no longer relies on manual guidance, enabling automated detection and localization. Additionally, we propose components such as Cross-view Feature Perception, Optimal Prompt Selection, and Cross-View Prompt Consistency, which facilitate cross-view perceptual learning and guide SAM to generate accurate masks. Extensive experimental results from five datasets (CASIA, Columbia, Coverage, IMD2020, and NIST16) validate the effectiveness of our proposed method.

cs.CV↗

arXiv2024

Weakly Supervised Temporal Action Localization via Dual-Prior Collaborative Learning Guided by Multimodal Large Language Models

Recent breakthroughs in Multimodal Large Language Models (MLLMs) have gained significant recognition within the deep learning community, where the fusion of the Video Foundation Models (VFMs) and Large Language Models(LLMs) has proven instrumental in constructing robust video understanding systems, effectively surmounting constraints associated with predefined visual tasks. These sophisticated MLLMs exhibit remarkable proficiency in comprehending videos, swiftly attaining unprecedented performance levels across diverse benchmarks. However, their operation demands substantial memory and computational resources, underscoring the continued importance of traditional models in video comprehension tasks. In this paper, we introduce a novel learning paradigm termed MLLM4WTAL. This paradigm harnesses the potential of MLLM to offer temporal action key semantics and complete semantic priors for conventional Weakly-supervised Temporal Action Localization (WTAL) methods. MLLM4WTAL facilitates the enhancement of WTAL by leveraging MLLM guidance. It achieves this by integrating two distinct modules: Key Semantic Matching (KSM) and Complete Semantic Reconstruction (CSR). These modules work in tandem to effectively address prevalent issues like incomplete and over-complete outcomes common in WTAL methods. Rigorous experiments are conducted to validate the efficacy of our proposed approach in augmenting the performance of various heterogeneous WTAL models.

cs.CV↗