Related papers: Study of micro-macro acceleration schemes for line…

We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…

Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale…

Micro- and nano-scale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an…

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve…

We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…

Stochastic model-based methods have received increasing attention lately due to their appealing robustness to the stepsize selection and provable efficiency guarantee. We make two important extensions for improving model-based methods on…

We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our…

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…

The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…

Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…