Related papers: Rational Construction of Stochastic Numerical Meth…
In this paper, we consider Langevin processes with mechanical constraints. The latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences. The results of this…
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…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
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…
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modeling approaches for the description of anomalous diffusion in biological systems, such as the very…
The key factor currently limiting the advancement of computational power of electronic computation is no longer the manufacturing density and speed of components, but rather their high energy consumption. While it has been widely argued…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…
We develop numerical schemes and sensitivity methods for stochastic models of proton transport that couple energy loss, range straggling and angular diffusion. For the energy equation we introduce a logarithmic Milstein scheme that…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
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…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final…
Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…
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…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
Sampling from probability distributions of the form $\sigma \propto e^{-\beta V}$, where $V$ is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when $V$ is…