Related papers: Consistent Point Orientation for Manifold Surfaces…

The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power…

We establish convergence results for a spatial semidiscretization of Mean Curvature Flow (MCF) for surfaces with fixed boundaries. Our analysis is based on Huisken's evolution equations for the mean curvature and the normal vector, enabling…

Estimating surface normals from 3D point clouds is critical for various applications, including surface reconstruction and rendering. While existing methods for normal estimation perform well in regions where normals change slowly, they…

We focus on estimating the 3D orientation of the ground plane from a single image. We formulate the problem as an inter-mingled multi-task prediction problem by jointly optimizing for pixel-wise surface normal direction, ground plane…

In recent years, point cloud normal estimation, as a classical and foundational algorithm, has garnered extensive attention in the field of 3D geometric processing. Despite the remarkable performance achieved by current Neural Network-based…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

We present the Global Neural World Model (GNWM), a self-stabilizing framework that achieves topological quantization through balanced continuous entropy constraints. Operating as a continuous, action-conditioned Joint-Embedding Predictive…

This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value problems with variable coefficients. To tackle problems with…

Several important problems in partial differential equations can be formulated as integral equations. Often the integral operator defines the solution of an elliptic problem with specified jump conditions at an interface. In principle the…

We construct global curves of rotational traveling wave solutions to the $2D$ water wave equations on a compact domain. The real analytic interface is subject to surface tension, while gravitational effects are ignored. In contrast to the…

This paper presents an effective normal estimation method adopting multi-patch stitching for an unstructured point cloud. The majority of learning-based approaches encode a local patch around each point of a whole model and estimate the…

In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the higher regularity of the free boundaries in obstacle-type…

We tackle the task of scene flow estimation from point clouds. Given a source and a target point cloud, the objective is to estimate a translation from each point in the source point cloud to the target, resulting in a 3D motion vector…

Point cloud completion aims to recover complete 3D geometry from partial observations caused by limited viewpoints and occlusions. Existing learning-based works, including 3D Convolutional Neural Network (CNN)-based, point-based, and…

We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…

Surrogate models are essential for fast and accurate surface pressure and friction predictions during design optimization of complex lifting surfaces. This study focuses on predicting pressure distribution over two-dimensional airfoils…

Point clouds collected by real-world sensors are always unaligned and sparse, which makes it hard to reconstruct the complete shape of object from a single frame of data. In this work, we manage to provide complete point clouds from sparse…

Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to…