Related papers: Optimizing the diffusion coefficient of overdamped…
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining…
We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…
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…
Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
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,…