Zhengqi Zhang

Jing Li, Zhengqi Zhang

We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $α\in(1,2)$. Conventional numerical methods for these equations often compromise the mesh-free advantage of Physics-Informed Neural Networks (PINNs) or impose high computational costs when computing fractional derivatives. The proposed method avoids first-order derivative calculations at quadrature points by introducing an integrand transformation technique, significantly reducing computational costs associated with fractional derivative evaluation while preserving accuracy. We conduct a comprehensive comparative analysis applying this integrand transformation in conjunction with both Monte Carlo integration and Gauss-Jacobi quadrature schemes across various time-fractional PDEs. Our results demonstrate that tDWfPINNs achieve superior computational efficiency without sacrificing accuracy. Furthermore, we incorporate the proposed approach into adaptive sampling approaches such as the residual-based adaptive distribution (RAD) for the time-fractional Burgers equation with order $α\in(1,2)$, which exhibits complex solution dynamics. The experiments show that the Gauss-Jacobi method typically outperforms the Monte Carlo approach; however, careful consideration is required when selecting the number of quadrature points. Overall, the proposed tDWfPINNs offer a significant advancement in the numerical solution of time-fractional diffusion-wave equations, providing an accurate and scalable mesh-free alternative for challenging fractional models.

Chenghao Gu, Zhenzhe Li, Zhengqi Zhang et al.

3D editing has shown remarkable capability in editing scenes based on various instructions. However, existing methods struggle with achieving intuitive, localized editing, such as selectively making flowers blossom. Drag-style editing has shown exceptional capability to edit images with direct manipulation instead of ambiguous text commands. Nevertheless, extending drag-based editing to 3D scenes presents substantial challenges due to multi-view inconsistency. To this end, we introduce DragScene, a framework that integrates drag-style editing with diverse 3D representations. First, latent optimization is performed on a reference view to generate 2D edits based on user instructions. Subsequently, coarse 3D clues are reconstructed from the reference view using a point-based representation to capture the geometric details of the edits. The latent representation of the edited view is then mapped to these 3D clues, guiding the latent optimization of other views. This process ensures that edits are propagated seamlessly across multiple views, maintaining multi-view consistency. Finally, the target 3D scene is reconstructed from the edited multi-view images. Extensive experiments demonstrate that DragScene facilitates precise and flexible drag-style editing of 3D scenes, supporting broad applicability across diverse 3D representations.