33 citations · 183 across the 19 of their papers we have counts for
23 papers
Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits
Andrey Pilipenko, Gilles Vilmart
We establish general conditions for the weak convergence of regular one-dimensional diffusion processes when their scale functions, speed measures, state spaces and boundary condit…
Reversible Stratonovich perturbations for accelerating convergence to equilibrium of Langevin dynamics
Guillaume Louis, Grigorios A. Pavliotis, Gilles Vilmart
In this paper, we study the problem of sampling from a probability distribution using Langevin-type dynamics. We consider overdamped Langevin dynamics perturbed by adding a Straton…
Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
Ibrahim Almuslimani, Gilles Vilmart, Konstantinos Zygalakis
Implicit methods are a natural approach for the integration of stiff differential equations, to avoid time-step restrictions faced by standard explicit integrators. Explicit stabil…
Arbitrary high order splitting methods for linear Schr{ö}dinger equations with non-trivial compatibility conditions
Joackim Bernier, Ramona Häberli, Gilles Vilmart
Splitting methods are a natural choice for the numerical time integration of partial differential equations, and arbitrary high order splitting schemes exist for Schr{ö}dinger equa…
SINDy for delay-differential equations: application to model bacterial zinc response
Antoine Sandoz, Verena Ducret, Georg A. Gottwald +2
We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differ…
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs
Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators ap…
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions
Guillaume Bertoli, Christophe Besse, Gilles Vilmart
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation…
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
Adrien Laurent, Gilles Vilmart
We derive a new methodology for the construction of high order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained…
Drift-preserving numerical integrators for stochastic Poisson systems
David Cohen, Gilles Vilmart
We perform a numerical analysis of a class of randomly perturbed {H}amiltonian systems and {P}oisson systems. For the considered additive noise perturbation of such systems, we sho…
Explicit stabilized integrators for stiff optimal control problems
Ibrahim Almuslimani, Gilles Vilmart
Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper,…
Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations
Assyr Abdulle, Grigorios A. Pavliotis, Gilles Vilmart
In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a s…
Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity
Guillaume Bertoli, Gilles Vilmart
The Strang splitting method, formally of order two, can suffer from order reduction when applied to semilinear parabolic problems with inhomogeneous boundary conditions. The recent…
Multirevolution integrators for differential equations with fast stochastic oscillations
Adrien Laurent, Gilles Vilmart
We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations the…
Highly-oscillatory problems with time-dependent vanishing frequency
Philippe Chartier, Mohammed Lemou, Florian Méhats +1
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below…
Explicit Stabilised Gradient Descent for Faster Strongly Convex Optimisation
Armin Eftekhari, Bart Vandereycken, Gilles Vilmart +1
This paper introduces the Runge-Kutta Chebyshev descent method (RKCD) for strongly convex optimisation problems. This new algorithm is based on explicit stabilised integrators for…
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations
Philippe Chartier, Mohammed Lemou, Florian Méhats +1
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-s…
Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations
Assyr Abdulle, Ibrahim Almuslimani, Gilles Vilmart
A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides w…
Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs
Adrien Laurent, Gilles Vilmart
We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the…
Asymptotic Preserving numerical schemes for multiscale parabolic problems
Nicolas Crouseilles, Mohammed Lemou, Gilles Vilmart
We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale . Numerical homogenization methods are…
Fast Langevin based algorithm for MCMC in high dimensions
Alain Durmus, Gareth O. Roberts, Gilles Vilmart +1
We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a…
High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise
Charles-Edouard Bréhier, Gilles Vilmart
We introduce a time-integrator to sample with high order of accuracy the invariant distribution for a class of semilinear SPDEs driven by an additive space-time noise. Combined wit…
Postprocessed integrators for the high order integration of ergodic SDEs
Gilles Vilmart
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over l…
Symplectic integrators in sub-Riemannian geometry: the Martinet case
Monique Chyba, Ernst Hairer, Gilles Vilmart
We compare the performances of symplectic and non-symplectic integrators for the computation of normal geodesics and conjugate points in sub-Riemannian geometry at the example of t…