Xinlong Feng

Anxiao Yu, Bangmin Wu, Zhengbang Zha et al.

The Monge-Ampère 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.

Haoran Zhou, Zhaohui Fu, Yangshuai Wang et al.

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.

Long Jing, Zhixiong Yang, Yajun Zhang et al.

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.