User profiles for Konstantinos C. Zygalakis
Konstantinos ZygalakisUniversity of Edinburgh Verified email at ed.ac.uk Cited by 2806 |
On the existence and the applications of modified equations for stochastic differential equations
KC Zygalakis�- SIAM Journal on Scientific Computing, 2011 - SIAM
In this paper we describe a general framework for deriving modified equations for stochastic
differential equations (SDEs) with respect to weak convergence. Modified equations are …
differential equations (SDEs) with respect to weak convergence. Modified equations are …
The connections between Lyapunov functions for some optimization algorithms and differential equations
JM Sanz Serna, KC Zygalakis�- SIAM Journal on Numerical Analysis, 2021 - SIAM
In this manuscript we study the properties of a family of a second-order differential equations
with damping, its discretizations, and their connections with accelerated optimization …
with damping, its discretizations, and their connections with accelerated optimization …
Exploration of the (non-) asymptotic bias and variance of stochastic gradient Langevin dynamics
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is
computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) …
computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) …
Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
JM Sanz-Serna, KC Zygalakis�- Journal of Machine Learning Research, 2021 - jmlr.org
We present a framework that allows for the non-asymptotic study of the 2-Wasserstein distance
between the invariant distribution of an ergodic stochastic differential equation and the …
between the invariant distribution of an ergodic stochastic differential equation and the …
Analysis of Brownian dynamics simulations of reversible bimolecular reactions
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which
include reversible bimolecular reactions is presented and analyzed. The method is a …
include reversible bimolecular reactions is presented and analyzed. The method is a …
High order numerical approximation of the invariant measure of ergodic SDEs
A Abdulle, G Vilmart, KC Zygalakis�- SIAM Journal on Numerical Analysis, 2014 - SIAM
We introduce new sufficient conditions for a numerical method to approximate with high order
of accuracy the invariant measure of an ergodic system of stochastic differential equations, …
of accuracy the invariant measure of an ergodic system of stochastic differential equations, …
Accelerating proximal Markov chain Monte Carlo by using an explicit stabilized method
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform
Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo …
Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo …
Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical
system, online, in order to improve estimation of the state of the system. Such methods are …
system, online, in order to improve estimation of the state of the system. Such methods are …
Uncertainty quantification in graph-based classification of high dimensional data
Classification of high dimensional data finds wide-ranging applications. In many of these
applications equipping the resulting classification with a measure of uncertainty may be as …
applications equipping the resulting classification with a measure of uncertainty may be as …
High weak order methods for stochastic differential equations based on modified equations
Inspired by recent advances in the theory of modified differential equations, we propose a
new methodology for constructing numerical integrators with high weak order for the time …
new methodology for constructing numerical integrators with high weak order for the time …