Related papers: Generating Transition Paths by Langevin Bridges
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
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…
We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by…
In generative modelling and stochastic optimal control, a central computational task is to modify a reference diffusion process to maximise a given terminal-time reward. Most existing methods require this reward to be differentiable, using…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
Transition state theory formally provides a simplifying approach for determining chemical reaction rates and pathways. Given an underlying potential energy surface for a reactive system, one can determine the dividing surface in phase space…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
A supersymmetric path integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the Langevin equation with inertia studied by Kramers, where N=2. The…
In this paper we present a formulation of the nonlinear stochastic differential equation which allows for systematic approximations. The method is not restricted to the asymptotic, i.e., stationary, regime but can be applied to derive…
The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a…
Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections)…
Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main…