Related papers: Instanton based importance sampling for rare event…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. If the fluid is turbulent, the statistics of the passive scalar exhibit complex behavior. This paper is concerned with…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
We address the question whether one can identify instantons in direct numerical simulations of the stochastically driven Burgers equation. For this purpose, we first solve the instanton equations using the Chernykh-Stepanov method [Phys.…
Sampling synthetic turbulent fields as a computationally tractable surrogate for direct numerical simulations (DNS) is an important practical problem in various applications, and allows to test our physical understanding of the main…
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…
In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…
Solving decision problems in complex, stochastic environments is often achieved by estimating the expected outcome of decisions via Monte Carlo sampling. However, sampling may overlook rare, but important events, which can severely impact…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm…
We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…
State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper,…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…