Related papers: Sobolev gradients and image interpolation

This paper introduces a projected Sobolev natural gradient descent (NGD) method for computing ground states of the Gross-Pitaevskii equation. By projecting a continuous Riemannian Sobolev gradient flow onto the normalized neural network…

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…

This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both…

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier--Stokes equations. Such methods, referred to as…

We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…

This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for…

We propose a class of very simple modifications of gradient descent and stochastic gradient descent. We show that when applied to a large variety of machine learning problems, ranging from logistic regression to deep neural nets, the…

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations.…

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…

Recovering the missing regions of an image is a task that is called image inpainting. Depending on the shape of missing areas, different methods are presented in the literature. One of the challenges of this problem is extracting features…

We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…

We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…

We propose a group sparse optimization model for inpainting of a square-integrable isotropic random field on the unit sphere, where the field is represented by spherical harmonics with random complex coefficients. In the proposed…

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…

Let $\Gamma$ be a graph endowed with a reversible Markov kernel $p$, and $P$ the associated operator, defined by $Pf(x)=\sum_y p(x,y)f(y)$. Denote by $\nabla$ the discrete gradient. We give necessary and/or sufficient conditions on $\Gamma$…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

In the first part of this contribution we prove the global existence and uniqueness of a trajectory that globally converges to the minimizer of the Gross-Pitaevskii energy functional for a large class of external potentials. Using the…

We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates…

Image inpainting refers to the restoration of an image with missing regions in a way that is not detectable by the observer. The inpainting regions can be of any size and shape. This is an ill-posed inverse problem that does not have a…