相关论文: Efficient Langevin sampling with position-dependen…

The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…

Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…

In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…

Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…

We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…

We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here,…

Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the…

This paper investigates the problem to determine whether a given stochastic process generates a sampled Brownian filtration. A fairly general sufficient condition is obtained by applying the Frank H. Clarke contraction criteria to a…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path integral method to compute the effective diffusion coefficient perturbatively to lowest order in the…