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A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…

Computation · Statistics 2023-11-01 Martin Chak , Nikolas Kantas , Tony Lelièvre , Grigorios A. Pavliotis

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…

Probability · Mathematics 2017-12-06 A. B. Duncan , N. Nuesken , G. A. Pavliotis

We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow…

Optimization and Control · Mathematics 2021-12-20 Xuefeng Gao , Zuo Quan Xu , Xun Yu Zhou

We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…

Mathematical Physics · Physics 2015-06-19 R. Joubaud , G. Pavliotis , G. Stoltz

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…

Statistical Mechanics · Physics 2025-03-19 Pyei Phyo Lin , Matthias Wächter , Joachim Peinke , M. Reza Rahimi Tabar

We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced;…

Dynamical Systems · Mathematics 2025-06-06 Ziming Liu , Andrew M. Stuart , Yixuan Wang

We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and F.…

Probability · Mathematics 2025-02-07 Giovanni Brigati , Francis Lörler , Lihan Wang

We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a…

Statistical Mechanics · Physics 2022-03-04 L. Costanzo , A. Lo Schiavo , A. Sarracino , M. Vitelli

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

Disordered Systems and Neural Networks · Physics 2026-03-17 Alessandro Zambon , Francesca Caruso , Riccardo Zecchina , Guido Tiana

Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…

Probability · Mathematics 2025-04-28 Axel Ringh , Akash Sharma

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…

Statistical Mechanics · Physics 2017-03-01 M. L. Rosinberg , G. Tarjus , T. Munakata

Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular simulations. Although their efficiency has been empirically…

Probability · Mathematics 2026-01-29 Tony Lelièvre , Xuyang Lin , Pierre Monmarché

The discretization of overdamped Langevin dynamics, through schemes such as the Euler-Maruyama method, can be corrected by some acceptance/rejection rule, based on a Metropolis-Hastings criterion for instance. In this case, the invariant…

Numerical Analysis · Mathematics 2016-07-06 Max Fathi , Gabriel Stoltz

We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a…

Machine Learning · Statistics 2022-05-24 Wei Deng , Guang Lin , Faming Liang

Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate…

Machine Learning · Statistics 2019-06-21 Soma Yokoi , Takuma Otsuka , Issei Sato

Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…

Statistics Theory · Mathematics 2025-11-04 Zhou Fan , Justin Ko , Bruno Loureiro , Yue M. Lu , Yandi Shen

We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…

Statistics Theory · Mathematics 2022-08-18 Wenlong Mou , Nhat Ho , Martin J. Wainwright , Peter Bartlett , Michael I. Jordan

The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for non-separable potentials. Theoretical results are lacking, and numerical calculation of the…

Mathematical Physics · Physics 2022-06-22 G. A. Pavliotis , G. Stoltz , U. Vaes

We present a novel method for drawing samples from Gibbs distributions with densities of the form $\pi(x) \propto \exp(-U(x))$. The method accelerates the unadjusted Langevin algorithm by introducing an inertia term similar to Polyak's…

Numerical Analysis · Mathematics 2025-10-09 Alexander Falk , Andreas Habring , Christoph Griesbacher , Thomas Pock

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 suitable Stratonovich perturbation that preserves the…

Numerical Analysis · Mathematics 2019-04-23 Assyr Abdulle , Grigorios A. Pavliotis , Gilles Vilmart