相关论文: Gradient-based optimization of 3D MHD equilibria

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…

Optimization and control of complex unsteady flows remains an important challenge due to the large cost of performing a function evaluation, i.e. a full computational fluid dynamics (CFD) simulation. Reducing the number of required function…

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…

In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

It is well-known that accelerated gradient first order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However,…

The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise…

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This…

In fusion reactor design, steels under consideration for the blanket are ferromagnetic, so the steel's effect on the plasma physics must be examined. For efficient calculation of these fields, we can exploit the fact that the magnetic…

We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…

The sharp increasing in fabrication capabilities of nanomaterials, and complex structures such as meta-surfaces and metalens, has opened to the possibility of employing them for accurately control the electromagnetic field, beyond the…

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-$C^1$ code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the…

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been…