相关论文: Bound preserving Point-Average-Moment PolynomiAl-i…

Using standard intrusive techniques when solving hyperbolic conservation laws with uncertainties can lead to oscillatory solutions as well as nonhyperbolic moment systems. The Intrusive Polynomial Moment (IPM) method ensures hyperbolicity…

This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem…

Transformers have demonstrated impressive results for 3D point cloud semantic segmentation. However, the quadratic complexity of transformer makes computation costs high, limiting the number of points that can be processed simultaneously…

Bundle adjustment (BA) with parallax angle based feature parameterization has been shown to have superior performance over BA using inverse depth or XYZ feature forms. In this paper, we propose an improved version of the parallax BA…

For gradient flows, the existing structure-preserving schemes are difficult to achieve arbitrary high-order accuracy in time while preserving maximum-principle (MBP) and energy dissipating simultaneously. In this paper, we develop a new…

Existing point cloud completion methods struggle to balance high-quality reconstruction with computational efficiency. To address this, we propose PPC-MT, a novel parallel framework for point cloud completion leveraging a hybrid…

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of…

U-shaped architectures have long dominated the field of medical image segmentation, while Transformers are widely employed for modeling long-range dependencies. The former typically handles scale variations implicitly by aggregating…

We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…

Central-upwind (CU) schemes are Riemann-problem-solver-free finite-volume methods widely applied to a variety of hyperbolic systems of PDEs. Exact solutions of these systems typically satisfy certain bounds, and it is highly desirable or…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

Mamba has recently gained widespread attention as a backbone model for point cloud modeling, leveraging a state-space architecture that enables efficient global sequence modeling with linear complexity. However, its lack of local inductive…

The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the well-known Allen-Cahn equation. While some commonly-used first-order time stepping schemes have turned out to preserve…

Recently, state space models have exhibited strong global modeling capabilities and linear computational complexity in contrast to transformers. This research focuses on applying such architecture to more efficiently and effectively model…

In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…

This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…

We survey developments, over the last thirty years, in the theory of Shape Preserving Approximation (SPA) by algebraic polynomials on a finite interval. In this article, "shape" refers to (finitely many changes of) monotonicity, convexity,…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

Transformers have become one of the foundational architectures in point cloud analysis tasks due to their excellent global modeling ability. However, the attention mechanism has quadratic complexity, making the design of a linear complexity…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…