相关论文: Mathematical foundations of Accelerated Molecular …

In this work, we introduce a simple modification of the Monte Carlo algorithm, which we call step Monte Carlo (sMC). The sMC approach allows to simulate processes far from equilibrium and obtain information about the dynamic properties of…

A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general but they satisfy an overdamped…

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…

Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

Calculating averages with respect to multimodal probability distributions is often necessary in applications. Markov chain Monte Carlo (MCMC) methods to this end, which are based on time averages along a realization of a Markov process…

Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…

The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…

Quasi-stationary distributions (QSD) have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are certainly…

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

This article is concerned with sampling from Gibbs distributions $\pi(x)\propto e^{-U(x)}$ using Markov chain Monte Carlo methods. In particular, we investigate Langevin dynamics in the continuous- and the discrete-time setting for such…

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but…

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…

In recent years, simulation methods based on the scaling of atomic potential functions, such as quasi-coarse-grained dynamics and coarse-grained dynamics, have shown promising results for modeling crystalline systems at multiple scales.…

Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…

This work presents a computationally lightweight motion planner for over-actuated platforms. For this purpose, a general state-space model for mobile platforms with several kinematic chains is defined, which considers non-linearities and…

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…