Related papers: Efficient estimation of rare-event kinetics
Markov State Modeling has recently emerged as a key technique for analyzing rare events in thermal equilibrium molecular simulations and finding metastable states. Here we export this technique to the study of friction, where strongly…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient…
In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
Detecting rare events, those defined to give rise to high impact but have a low probability of occurring, is a challenge in a number of domains including meteorological, environmental, financial and economic. The use of machine learning to…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
This paper considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for e.g. modelling of credit risk. Previous attempts at designing importance sampling algorithms…
Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
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…