Related papers: Differentiable Computational Geometry for 2D and 3…

A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…

Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…

The formation of the large-scale structure, the evolution and distribution of galaxies, quasars, and dark matter on cosmological scales, requires numerical simulations. Differentiable simulations provide gradients of the cosmological…

To enable heterogeneous computing systems with autonomous programming and optimization capabilities, we propose a unified, end-to-end, programmable graph representation learning (PGL) framework that is capable of mining the complexity of…

Deep learning for molecular science has so far mainly focused on 2D molecular graphs. Recently, however, there has been work to extend it to 3D molecular geometry, due to its scientific significance and critical importance in real-world…

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between…

The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…

Deep neural networks (DNNs) have shown remarkable performance improvements on vision-related tasks such as object detection or image segmentation. Despite their success, they generally lack the understanding of 3D objects which form the…

Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable…

We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…

Recently, Graph Convolutional Networks (GCNs) have been widely studied for graph-structured data representation and learning. However, in many real applications, data are coming with multiple graphs, and it is non-trivial to adapt GCNs to…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in…

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…

We introduce cilantro, an open-source C++ library for geometric and general-purpose point cloud data processing. The library provides functionality that covers low-level point cloud operations, spatial reasoning, various methods for point…

Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…

Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method that…

In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…

Many machine learning models operate on images, but ignore the fact that images are 2D projections formed by 3D geometry interacting with light, in a process called rendering. Enabling ML models to understand image formation might be key…