arXiv subjects

Xinlong Feng

Publications and source records attributed to Xinlong Feng.

5 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Networks with Attention Feature Expansion for Monge-Amp\`ere Equations

The Monge-Amp\`ere equation is a fundamental fully nonlinear elliptic partial differential equation that finds extensive applications across multiple disciplines. This study proposes a novel physics-informed neural network integrated with attention feature expansion (PINN-AFE) for its numerical solution. A multi-head attention enhanced feature pool is constructed to enable adaptive nonlinear feature representation, and input convex neural networks are adopted to impose strict convexity of solutions with rigorous theoretical guarantees. Meanwhile, a dynamically weighted loss function combined with hybrid optimization is formulated to accelerate training convergence. Comprehensive numerical experiments validate the accuracy and computational efficiency of the developed framework. The PINN-AFE paradigm is further extended to image processing tasks, delivering high-quality and physically consistent results in both image enhancement and medical image registration scenarios.

math.NA↗

arXiv2026

A Discrete-Time Random Feature Method for Nonlinear Evolution Equations with Implicit-Explicit Runge--Kutta Time Stepping

We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable, the method advances the solution step by step, with each time level computed from previously available states. The spatial solution at each step is represented in the random feature trial space, and the time discretization is given by an implicit-explicit Runge--Kutta (IMEX-RK, 4 stages, third-order) scheme. After splitting the operator into linear and nonlinear parts, each stage admits a linear least-squares formulation, which avoids nonlinear least-squares solves. We also derive a global error estimate for the fully discrete method, separating the contributions of the stage-wise RFM approximation, perturbations in the least-squares coefficients, and the temporal discretization. Numerical experiments for the Allen--Cahn, Burgers, Korteweg--De Vries, and Cahn--Hilliard equations show relative $L^2$-errors of order $10^{-6}$ and convergence rates consistent with the third-order IMEX scheme. A comparison with an IMEX-PINN variant shows that the proposed method achieves higher accuracy at substantially lower computational cost.

math.NA↗

arXiv2026

Contrastive Learning for Multimodal Human Activity Recognition with Limited Labeled Data

Human activity recognition serves as the foundation for various emerging applications. In recent years, researchers have used collaborative sensing of multi-source sensors to capture complex and dynamic human activities. However, multimodal human activity sensing typically encounters highly heterogeneous data across modalities and label scarcity, resulting in an application gap between existing solutions and real-world needs. In this paper, we propose CLMM, a general contrastive learning framework for human activity recognition that achieves effective multimodal recognition with limited labeled data. CLMM employs a novel two-stage training strategy. In the first stage, CLMM employs a CNN-DiffTransformer encoder to capture cross-modal shared information by extracting local and global features. Meanwhile, a hard-positive samples weighting algorithm enhances gradient propagation to reinforce shared learning. In the second stage, a dual-branch architecture combining quality-guided attention and bidirectional gated units captures modality-specific information, while a primary-auxiliary collaborative training strategy fuses both shared and modality-specific information. Experimental results on three public datasets demonstrate that CLMM significantly improves state-of-the-art baselines in both recognition accuracy and convergence performance.

cs.LG↗

arXiv2023

Error estimates for the highly efficient and energy stable schemes for the 2D/3D two-phase MHD

In this paper, we mainly focus on the rigorous convergence analysis of two fully decoupled, unconditionally energy-stable methods for the diffuse interface two-phase magnetohydrodynamics (MHD) model. The two methods consist of the semi-implicit stabilization method and the invariant energy quadratization (IEQ) method, which are both applied to the phase field system. In addition, the pressure correction method is used for the saddle point system, and appropriate implicit-explicit treatments are employed for the nonlinear coupled terms. We prove the unconditional energy stability of the two schemes. In addition, we mainly establish the error estimates based on the bounds of $\left\|\phi^{k}\right\|_{L^{\infty}}$ and $\left\|\textbf{b}^{k}\right\|_{L^{\infty}}$. Several numerical examples are presented to test the accuracy and stability of the proposed methods.

math.AP↗

arXiv2021

Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle

Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initial and boundary conditions and nonlinear operator preserves for all time a uniform pointwise bound in absolute value. It has been a challenging problem on how to design unconditionally MBP-preserving high-order accurate time-stepping schemes for these equations. In this paper, we combine the integrating factor Runge-Kutta (IFRK) method with the linear stabilization technique to develop a stabilized IFRK (sIFRK) method, and successfully derive sufficient conditions for the proposed method to preserve MBP unconditionally in the discrete setting. We then elaborate some sIFRK schemes with up to the third-order accuracy, which are proven to be unconditionally MBP-preserving by verifying these conditions. In addition, it is shown that many classic strong stability-preserving sIFRK schemes do not satisfy these conditions except the first-order one. Extensive numerical experiments are also carried out to demonstrate the performance of the proposed method.

math.NA↗