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We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…
We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the…
Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventiona l simulation run. Over the past several decades, specialised simulation methods…
Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole…
We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to efficiently measure transition times in rare-event processes in non-equilibrium systems, and apply it to study the first-order (discontinuous) kinetic transition in the…
Forward-flux sampling (FFS) is a path sampling technique that has gained increased popularity in recent years, and has been used to compute rates of rare event phenomena such as crystallization, condensation, hydrophobic evaporation, DNA…
Forward flux sampling (FFS) provides a convenient and efficient way to simulate rare events in equilibrium or non-equilibrium systems. FFS ratchets the system from an initial state to a final state via a series of interfaces in phase space.…
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…
The purpose of this paper is to develop a new fractional dynamical approach to superstatistics. Namely, we show that superstatistical distribution functions can be obtained from stationary solutions of the generalized Fokker-Planck equation…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
Rare event simulation and estimation for systems in equilibrium are among the most challenging topics in molecular dynamics. As was shown by Jarzynski and others, nonequilibrium forcing can theoretically be used to obtain equilibrium rare…
Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of so-called rare events that are characterized by transitions between metastable states separated by sizeable free energy barriers. Their…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
Stochastic interacting particle systems are widely used to model collective phenomena across diverse fields, including statistical physics, biology, and social dynamics. The McKean-Vlasov equation arises as the mean-field limit of such…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
Non-stationary forced oscillations (FOs) have been observed in power system operations. However, most detection methods assume that the frequency of FOs is stationary. In this paper, we present a methodology for the analysis of…
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…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…