Weiying Zheng

Situan Li, Weiying Zheng

We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces, with arbitrary fixed Sobolev order k >= 1, on fitted interface meshes. The cells are coordinate-compatible cuboids, the local spaces are Q_{p_K}(K) with arbitrary elementwise degrees satisfying p_K >= 2k-1, and the coefficient may have arbitrarily large jumps across material interfaces. Under local coefficient oscillation bounds and a local high-side connectivity condition, both the conforming H^k space and the nonconforming spaces V_h^{(s)}, 0 <= s <= k, admit stable decompositions with constants which may depend on the fixed parameters d and k, but are independent of the mesh size, all polynomial degrees, neighboring degree ratios, and the global coefficient contrast. The argument combines a Hermite endpoint transform for endpoint jets of order 0,...,k-1, its tensor-product extension, weighted broken patch Poincare inequalities, and a successive correction of normal derivative jumps. Numerical experiments for a three-dimensional DG problem with large coefficient jumps and strongly varying local polynomial degrees support the predicted robustness. For k = 1 the same conclusions hold on uniformly regular mapped cubical meshes whose neighboring element maps agree on each common face.

Situan Li, Weiying Zheng

We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of reaction-diffusion and fitted-interface problems. On conforming simplicial meshes in arbitrary dimension, the single-domain result allows an arbitrary elementwise degree distribution subject only to $p_K\ge1$. A minimal-average Falk--Winther bubble transform is introduced by taking each subsimplex average over a fixed adjacent element of minimal polynomial degree. The resulting components remain in the prescribed variable-degree space and satisfy $L^2$- and $H^1$-stable estimates with constants independent of the mesh size, the polynomial degrees, and the way the degrees vary from element to element. Together with a stable continuous piecewise affine component, this yields an $hp$-uniform Schwarz preconditioner for single-domain reaction-diffusion problems with locally comparable coefficients. For three-dimensional fitted-interface problems, we use a symmetric Nitsche discretization on a tetrahedral mesh fitted to a piecewise planar interface. Surface jump components are lifted into the side selected by the penalty scaling, and the conforming remainder is decomposed by a weighted one-sided bubble transform. Grouping the components by vertices gives a practical vertex-patch Schwarz preconditioner. Under a common-degree condition on interface-touching tetrahedra, the condition number is bounded independently of the mesh size, the local polynomial degrees, the diffusion contrast, and the coefficient magnitudes. Numerical experiments for pure diffusion problems support the theory and suggest robustness beyond the common-degree assumption.

Xinjie Jiang, Chenxi Zheng, Xuemiao Xu et al.

Video Visual Relation Detection (VidVRD) focuses on understanding how entities interact over time and space in videos, a key step for gaining deeper insights into video scenes beyond basic visual tasks. Traditional methods for VidVRD, challenged by its complexity, typically split the task into two parts: one for identifying what relation categories are present and another for determining their temporal boundaries. This split overlooks the inherent connection between these elements. Addressing the need to recognize entity pairs' spatiotemporal interactions across a range of durations, we propose VrdONE, a streamlined yet efficacious one-stage model. VrdONE combines the features of subjects and objects, turning predicate detection into 1D instance segmentation on their combined representations. This setup allows for both relation category identification and binary mask generation in one go, eliminating the need for extra steps like proposal generation or post-processing. VrdONE facilitates the interaction of features across various frames, adeptly capturing both short-lived and enduring relations. Additionally, we introduce the Subject-Object Synergy (SOS) module, enhancing how subjects and objects perceive each other before combining. VrdONE achieves state-of-the-art performances on the VidOR benchmark and ImageNet-VidVRD, showcasing its superior capability in discerning relations across different temporal scales. The code is available at https://github.com/lucaspk512/vrdone.

Situan Li, Weiying Zheng

Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed edge and face traces must be preserved while a polynomial is extended into a neighboring cell or boundary patch. The main contribution of this paper is the construction of p-robust polynomial liftings on nonsingular conforming hexahedral boundary patches, with stable control of both the H^1 norm and the H^1-seminorm estimates needed for energy arguments. These liftings imply H^1-seminorm stable discrete harmonic extensions of polynomial Dirichlet traces. They also serve as boundary corrections for the conforming hp Clement interpolant, yielding trace-preserving interpolation operators for functions with only H^1 regularity. Under the uniform boundary-degree condition the constants are p-uniform; in the non-uniform case the stated logarithmic loss appears. We also treat meshes that may contain conforming singular boundary patches, where the loss remains polylogarithmic in the maximal local degree. Trace-preserving interpolation on reference cells and vertex-supported decompositions are developed as local tools for these patch and mesh-level constructions.

Situan Li, Weiying Zheng

We construct p-robust polynomial trace liftings on three-dimensional tetrahedral meshes. The prescribed trace is a continuous piecewise polynomial function on a boundary face patch; the tetrahedra touching this patch have one common degree, while the interior degrees may be arbitrary. The lifting is degree-preserving, supported in the corresponding boundary layer, and satisfies both an H^1 estimate and a scaled boundary-layer L^2 estimate with constants independent of the mesh size and the polynomial degree. The construction is local and combines tetrahedral polynomial liftings, face-gluing arguments, and nonsingular vertex patches. As consequences of the construction, we obtain p-robust discrete harmonic extensions, including an H^1-seminorm-stable extension for the pure diffusion energy, and a boundary-preserving hp interpolation operator that keeps piecewise polynomial Dirichlet data exactly while retaining standard local approximation estimates.

Ralf Hiptmair, Weiying Zheng

We consider H(curl)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H1-context along with local discrete Helmholtz-type decompositions of the edge element space.

Xue Jiang, Peijun Li, Junliang Lv et al.

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing an equivalent transparent boundary condition. Second, an a posteriori error estimate is deduced for the discrete problem and is used to determine the finite elements for refinements and to determine the PML parameters. Numerical experiments are included to demonstrate the competitive behavior of the proposed adaptive method.

Xue Jiang, Peijun Li, Junliang Lv et al.

This paper is concerned with the analysis of elastic wave scattering of a time-harmonic plane wave by a biperiodic rigid surface, where the wave propagation is governed by the three-dimensional Navier equation. An exact transparent boundary condition is developed to reduce the scattering problem equivalently into a boundary value problem in a bounded domain. The perfectly matched layer (PML) technique is adopted to truncate the unbounded physical domain into a bounded computational domain. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing a PML equivalent transparent boundary condition. The proofs rely on a careful study of the error between the two transparent boundary operators. The work significantly extend the results from the one-dimensional periodic structures to the two-dimensional biperiodic structures. Numerical experiments are included to demonstrate the competitive behavior of the proposed method.

Xue Jiang, Peijun Li, Junliang Lv et al.

Consider the diffraction of an electromagnetic plane wave by a biperiodic structure where the wave propagation is governed by the three-dimensional Maxwell equations. Based on transparent boundary condition, the grating problem is formulated into a boundary value problem in a bounded domain. Using a duality argument technique, we derive an a posteriori error estimate for the finite element method with the truncation of the nonlocal Dirichlet-to-Neumann (DtN) boundary operator. The a posteriori error consists of both the finite element approximation error and the truncation error of boundary operator which decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is developed with error controlled by the a posterior error estimate, which determines the truncation parameter through the truncation error and adjusts the mesh through the finite element approximation error. Numerical experiments are presented to demonstrate the competitive behavior of the proposed adaptive method.

Wenlong Wan, Weiying Zheng, Tianyi Xiang et al.

We introduce the task of Audible Action Temporal Localization, which aims to identify the spatio-temporal coordinates of audible movements. Unlike conventional tasks such as action recognition and temporal action localization, which broadly analyze video content, our task focuses on the distinct kinematic dynamics of audible actions. It is based on the premise that key actions are driven by inflectional movements; for example, collisions that produce sound often involve abrupt changes in motion. To capture this, we propose $TA^{2}Net$, a novel architecture that estimates inflectional flow using the second derivative of motion to determine collision timings without relying on audio input. $TA^{2}Net$ also integrates a self-supervised spatial localization strategy during training, combining contrastive learning with spatial analysis. This dual design improves temporal localization accuracy and simultaneously identifies sound sources within video frames. To support this task, we introduce a new benchmark dataset, $Audible623$, derived from Kinetics and UCF101 by removing non-essential vocalization subsets. Extensive experiments confirm the effectiveness of our approach on $Audible623$ and show strong generalizability to other domains, such as repetitive counting and sound source localization. Code and dataset are available at https://github.com/WenlongWan/Audible623.

Weiying Zheng, Ziyue Lin, Pengxin Guo et al.

Vision-Language Models (VLMs) have demonstrated remarkable capabilities in cross-modal understanding and generation by integrating visual and textual information. While instruction tuning and parameter-efficient fine-tuning methods have substantially improved the generalization of VLMs, most existing approaches rely on centralized training, posing challenges for deployment in domains with strict privacy requirements like healthcare. Recent efforts have introduced Federated Learning (FL) into VLM fine-tuning to address these privacy concerns, yet comprehensive benchmarks for evaluating federated fine-tuning strategies, model architectures, and task generalization remain lacking. In this work, we present \textbf{FedVLMBench}, the first systematic benchmark for federated fine-tuning of VLMs. FedVLMBench integrates two mainstream VLM architectures (encoder-based and encoder-free), four fine-tuning strategies, five FL algorithms, six multimodal datasets spanning four cross-domain single-task scenarios and two cross-domain multitask settings, covering four distinct downstream task categories. Through extensive experiments, we uncover key insights into the interplay between VLM architectures, fine-tuning strategies, data heterogeneity, and multi-task federated optimization. Notably, we find that a 2-layer multilayer perceptron (MLP) connector with concurrent connector and LLM tuning emerges as the optimal configuration for encoder-based VLMs in FL. Furthermore, current FL methods exhibit significantly higher sensitivity to data heterogeneity in vision-centric tasks than text-centric ones, across both encoder-free and encoder-based VLM architectures. Our benchmark provides essential tools, datasets, and empirical guidance for the research community, offering a standardized platform to advance privacy-preserving, federated training of multimodal foundation models.

Lingxiao Li, Weiying Zheng

In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the pressure are approximated by H1-conforming finite elements, while the magnetic field is approximated by H(curl)-conforming edge elements. An efficient preconditioner is proposed to accelerate the convergence of the GMRES method for solving the linearized MHD problem. We use three numerical experiments to demonstrate the effectiveness of the finite element method and the robustness of the discrete solver. The preconditioner contains the least undetermined parameters and is optimal with respect to the number of degrees of freedom. We also show the scalability of the solver for moderate physical parameters.