Related papers: Spatially-varying meshless approximation method fo…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems (IPS) {and the associated…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The…
Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical…
Stencil computations represent a very common class of nested loops in scientific and engineering applications. Exploiting vector units in modern CPUs is crucial to achieving peak performance. Previous vectorization approaches often consider…
In this paper, a rapid approximation method is introduced to estimate the sea surface velocity field based on scattered measurements. The method uses a simplified two-dimensional flow model as a surrogate model, which mimics the real…
This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy-Navier equation, using a strong form method based on a local Weighted Least Squares (WLS) approximation. The main advantage of the employed…
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…
A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
We study the stochastic total variation flow (STVF) equation with linear multiplicative noise. By considering a limit of a sequence of regularized stochastic gradient flows with respect to a regularization parameter $\varepsilon$ we obtain…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…