Related papers: P2M++: Enhanced Solver for Point-to-Mesh Distance …

Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…

Determining the relative pose of a previously unseen object between two images is pivotal to the success of generalizable object pose estimation. Existing approaches typically predict 3D translation utilizing the ground-truth object…

In this paper, we introduce Point2Mesh, a technique for reconstructing a surface mesh from an input point cloud. Instead of explicitly specifying a prior that encodes the expected shape properties, the prior is defined automatically using…

Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…

Existing convolutional learning methods for 3D point cloud data are divided into two paradigms: point-based methods that preserve geometric precision but often face performance challenges, and voxel-based methods that achieve high…

We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…

In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new…

We propose a novel concept of asymmetric feature maps (AFM), which allows to evaluate multiple kernels between a query and database entries without increasing the memory requirements. To demonstrate the advantages of the AFM method, we…

Large Language Models (LLMs) exhibit strong reasoning abilities, but their high computational costs limit their practical deployment. Recent studies reveal significant redundancy in LLMs layers, making layer pruning an active research…

We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…

In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in…

Timeseries monitoring systems such as Prometheus play a crucial role in gaining observability of the underlying system components. These systems collect timeseries metrics from various system components and perform monitoring queries over…

Deep learning-based object recognition systems can be easily fooled by various adversarial perturbations. One reason for the weak robustness may be that they do not have part-based inductive bias like the human recognition process.…

We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise…

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of…

Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate…

Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…

Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces,…