Related papers: A meshfree exterior calculus for generalizable and…

The problem of solving partial differential equations (PDEs) on manifolds can be considered to be one of the most general problem formulations encountered in computational multi-physics. The required covariant forms of balance laws as well…

Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained…

Mobile edge computing (MEC) is a promising approach for enabling cloud-computing capabilities at the edge of cellular networks. Nonetheless, security is becoming an increasingly important issue in MEC-based applications. In this paper, we…

Point completion refers to completing the missing geometries of an object from incomplete observations. Main-stream methods predict the missing shapes by decoding a global feature learned from the input point cloud, which often leads to…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional…

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also…

Each scanner possesses its unique characteristics and exhibits its distinct sampling error distribution. Training a network on a dataset that includes data collected from different scanners is less effective than training it on data…

This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…

Point clouds obtained from 3D scans are typically sparse, irregular, and noisy, and required to be consolidated. In this paper, we present the first deep learning based edge-aware technique to facilitate the consolidation of point clouds.…

We present a framework for the structure-preserving approximation of partial differential equations on mapped multipatch domains, extending the classical theory of finite element exterior calculus (FEEC) to discrete de Rham sequences which…

We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contrasts current approaches for "neural PDE solvers" that employ…

The significant effort required to annotate data for new training datasets hinders computer vision research and machine learning in the construction industry. This work explores adapting standard datasets and the latest transformer model…

This paper presents a novel end-to-end Learned Point Cloud Geometry Compression (a.k.a., Learned-PCGC) framework, to efficiently compress the point cloud geometry (PCG) using deep neural networks (DNN) based variational autoencoders (VAE).…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we…

We present a meshfree collocation scheme to discretize intrinsic surface differential operators over scalar fields on smooth curved surfaces with given normal vectors and a non-intersecting tubular neighborhood. The method is based on…

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…

Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…

Ground segmentation of point clouds remains challenging because of the sparse and unordered data structure. This paper proposes the GSECnet - Ground Segmentation network for Edge Computing, an efficient ground segmentation framework of…