Ruoxia Yao

Physics-informed neural networks (PINNs) offer a flexible framework for solving partial differential equations (PDEs), yet they typically struggle with multi-frequency dynamics, nonlinear interactions, and optimization instability, especially in high-dimensional settings. To address these issues, we propose KAT-PINNs, a novel hybrid architecture that integrates a Morlet-wavelet-based high-dimensional mapper, a KAN-enhanced Transformer encoder, and a Residual-Based Attention (RBA) mechanism. The wavelet mapper provides a high-dimensional mixed embedding of the spatiotemporal inputs, the encoder module-within which wav-KAN serves as the nonlinear transformation enhances expressiveness, and the RBA adaptively focuses optimization on high-residual regions to improve stability. We evaluate the proposed framework on several PDEs, with particular emphasis on high-dimensional nonlinear equations used to describe complex wave behaviors. Experimental results show that KAT-PINNs consistently outperforms baseline models, reducing relative errors by up to 40% - 70% across problems of varying dimensionality while achieving faster convergence and more stable reconstruction of multi-frequency spatiotemporal structures.

Physics-informed neural networks (PINNs) offer a flexible framework for solving partial differential equations (PDEs), yet they typically struggle with multi-frequency dynamics, nonlinear interactions, and optimization instability, especially in high-dimensional settings. To address these issues, we propose KAT-PINNs, a novel hybrid architecture that integrates a Morlet-wavelet-based high-dimensional mapper, a KAN-enhanced Transformer encoder, and a Residual-Based Attention (RBA) mechanism. The wavelet mapper provides a high-dimensional mixed embedding of the spatiotemporal inputs, the encoder module-within which wav-KAN serves as the nonlinear transformation enhances expressiveness, and the RBA adaptively focuses optimization on high-residual regions to improve stability. We evaluate the proposed framework on several PDEs, with particular emphasis on high-dimensional nonlinear equations used to describe complex wave behaviors. Experimental results show that KAT-PINNs consistently outperforms baseline models, reducing relative errors by up to 40% - 70% across problems of varying dimensionality while achieving faster convergence and more stable reconstruction of multi-frequency spatiotemporal structures.

The phenomenon of shallow water waves in nature attracts the attention of scholars and plays an important role in fields such as marine ecology, tidal waves, solitary waves, and offshore engineering. To better understand the phenomenon of shallow water waves, we investigate the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (2D-CDGKS) equation from the perspective of integrable decomposition. By utilizing the Lax pairs and formal variable separation (FVS) method, the 2D-CDGKS equation can be decomposed into the Sharma-Tasso-Olver (STO) equation, the integrable Svinolupov-Sokolov (SS) equation, and the Sawada-Kotera (SK) equation etc. We construct some novel exact solutions by linear superposing the integrable decomposition relations. Additionally, the superposition of two-soliton solution with three-soliton solution, two-soliton solution propagating on periodic cnoidal background waves, and soliton-cnoidal wave interaction solutions with interesting dynamics, are explored. Our results have important significance for understanding of the physical events consolidate the complex system under consideration and offering vital insights into the intricate dynamics of its behavior. Furthermore, the present work will enrich the investigation of nonlinear dynamics in high-dimensional nonlinear system, and provide theoretical support for the related experimental phenomena.

Purpose: Estimation of Fiber Orientation Distribution (FOD) is an essential step in tractography. However, traditional reconstruction methods such as Multi‐shell Multi‐Tissue Constrained Spherical Deconvolution (MSMT‐CSD) are demanding in terms of data quality and hardware equipment, limiting their application to low‐angle resolution data. Deep learning has demonstrated significant potential for fiber orientation distribution reconstruction in recent years. Nevertheless, there is still room for improvement in the models, particularly in terms of reconstruction accuracy and the retention of fine details. This study aims to develop an efficient and reliable deep‐ learning framework to improve the accuracy of fiber orientation distribution reconstruction, namely, the Dual‐Branch Feature Fusion Network (DBFF‐Net).Methods: DBFF‐Net learns the key features of high angular resolution FOD through a multi‐branch network architecture, which incorporates high‐quality MSMT‐CSD data as the target during the training process, and by fusing multi‐scale feature information, significantly improves the FOD reconstruction performance of Low Angular Resolution Diffusion Imaging (LARDI) data.Results: The experimental results show that DBFF‐Net surpasses existing traditional and deep‐learning methods across multiple metrics, particularly in the fiber crossing regions and under LARDI data conditions.Conclusion: DBFF‐Net provides an efficient and reliable FOD reconstruction scheme and offers a new white matter fiber imaging tool in clinical and scientific research.

Diffusion magnetic resonance imaging (dMRI) currently stands as the foremost noninvasive method for quantifying brain tissue microstructure and reconstructing white matter fiber pathways. However, the inherent free diffusion motion of water molecules in dMRI results in signal decay, diminishing the signal-to-noise ratio (SNR) and adversely affecting the accuracy and precision of microstructural data. In response to this challenge, we propose a novel method known as the Multiscale Fast Attention-Multibranch Irregular Convolutional Neural Network for dMRI image denoising. In this work, we introduce Multiscale Fast Channel Attention, a novel approach for efficient multiscale feature extraction with attention weight computation across feature channels. This enhances the model’s capability to capture complex features and improves overall performance. Furthermore, we propose a multi-branch irregular convolutional architecture that effectively disrupts spatial noise correlation and captures noise features, thereby further enhancing the denoising performance of the model. Lastly, we design a novel loss function, which ensures excellent performance in both edge and flat regions. Experimental results demonstrate that the proposed method outperforms other state-of-the-art deep learning denoising methods in both quantitative and qualitative aspects for dMRI image denoising with fewer parameters and faster operational speed.

The (2 + 1)-dimensional generalized fifth-order KdV (2GKdV) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero background wave on the multiple soliton solution of the 2GKdV equation, breather waves are constructed, for which some transformed wave conditions are considered that yield abundant novel nonlinear waves including X/Y-Shaped (XS/YS), asymmetric M-Shaped (MS), W-Shaped (WS), Space-Curved (SC) and Oscillation M-Shaped (OMS) solitons. Furthermore, distinct nonlinear wave molecules and interactional structures involving the asymmetric MS, WS, XS/YS, SC solitons, and breathers, lumps are constructed after considering the corresponding existence conditions. The dynamical properties of the nonlinear molecular waves and interactional structures are revealed via analyzing the trajectory equations along with the change of the phase shifts.