Related papers: Combining high-order metric interpolation and geom…

Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…

Generalizable 3D object reconstruction from single-view RGB-D images remains a challenging task, particularly with real-world data. Current state-of-the-art methods develop Transformer-based implicit field learning, necessitating an…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes and produces in one go, i.e. in a single feed forward pass, a smooth interpolation and point-to-point correspondences between them. The…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these…

Building good 3D maps is a challenging and expensive task, which requires high-quality sensors and careful, time-consuming scanning. We seek to reduce the cost of building good reconstructions by correcting views of existing low-quality…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local…

In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…

We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…

We present an $hr$-adaptivity framework for optimization of high-order meshes. This work extends the $r$-adaptivity method for mesh optimization by Dobrev et al., where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize…

We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…

We present a novel method to model and calculate deformation fields between shapes embedded in $\mathbb{R}^D$. Our framework combines naturally interpolating the two input shapes and calculating correspondences at the same time. The key…

We describe a general approach for constructing a broad class of operators approximating high-dimensional curves based on geometric Hermite data. The geometric Hermite data consists of point samples and their associated tangent vectors of…

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…

We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…