Related papers: A vertex-weighted-Least-Squares gradient reconstru…

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…

A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…

Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, a popular method is the stochastic gradient descent. Viewed as a process for sampling the loss…

Multi-view mesh reconstruction remains a core challenge in computer graphics and vision, especially for recovering high-frequency geometry from sparse observations. Recent methods such as 3D Gaussian Splatting (3DGS) and Neural Radiance…

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear…

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite…

One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…

This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…

This paper proposes GradientSurf, a novel algorithm for real time surface reconstruction from monocular RGB video. Inspired by Poisson Surface Reconstruction, the proposed method builds on the tight coupling between surface, volume, and…

In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…

An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flow with the quasi-conservative interface…

Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…

A novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary…

This paper presents a minimalist neural regression network as an aggregate of independent identical regression blocks that are trained simultaneously. Moreover, it introduces a new multiplicative parameter, shared by all the neural units of…

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…