Related papers: Convergence analysis of a parareal algorithm with …
As deep neural networks (DNNs) become deeper, the training time increases. In this perspective, multi-GPU parallel computing has become a key tool in accelerating the training of DNNs. In this paper, we introduce a novel methodology to…
Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm…
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse…
Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical…
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…
We present a novel feature matching algorithm that systematically utilizes the geometric properties of features such as position, scale, and orientation, in addition to the conventional descriptor vectors. In challenging scenes with the…