Related papers: Exponential time propagators for elastodynamics
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
High order exponential integrators require computing linear combination of exponential like $\varphi$-functions of large matrices $A$ times a vector $v$. Krylov projection methods are the most general and remain an efficient choice for…
We investigate the integration of Nesterov-type acceleration into primal-dual methods for structured convex optimization. While proximal splitting algorithms efficiently handle composite problems of the form $\min_x f(x)+g(x)+h(Kx)$,…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
We are interested in the simulation of open quantum systems governed by the Lindblad master equation in an infinite-dimensional Hilbert space. To simulate the solution of this equation, the standard approach involves two sequential…
The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. The popular numerical methods for these models require very small time steps to ensure stability. Our objective is to formulate and test two…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…
Two-time-scale stochastic approximation algorithms are iterative methods used in applications such as optimization, reinforcement learning, and control. Finite-time analysis of these algorithms has primarily focused on fixed point…
In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…
In this paper, we study distributed optimization with smooth non-convex local objectives. We propose a novel variant of the well-known EXact firsT-ordeR Algorithm (EXTRA), called Two-timescale EXTRA, by introducing two distinct step-sizes.…
This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional…
We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is…