Related papers: Solving Langevin equation with the bicolour rooted…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
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;…
We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{\alpha\beta}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing…
We study Langevin dynamics with a kinetic energy different from the standard, quadratic one in order to accelerate the sampling of Boltzmann-Gibbs distributions. In particular, this kinetic energy can be non-globally Lipschitz, which raises…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the…
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin…
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the…
We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the…
Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reductive Lie groups provide the setting in which the Lie group…
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…