Related papers: Doob's Lagrangian: A Sample-Efficient Variational …
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…
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understand the mechanism of…
We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow…
Rare event sampling algorithms are essential for understanding processes that occur infrequently on the molecular scale, yet they are important for the long-time dynamics of complex molecular systems. One of these algorithms, transition…
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
To improve safety and energy efficiency, autonomous vehicles are expected to drive smoothly in most situations, while maintaining their velocity below a predetermined speed limit. However, some scenarios such as low road adherence or…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We propose exact solution approaches for a lateral transhipment problem which, given a pre-specified sequence of customers, seeks an optimal inventory redistribution plan considering travel costs and profits dependent on inventory levels.…
We study the long-time behaviour of the first-moment semigroup of a non conservative piecewise deterministic measure-valued stochastic process with support on R 2 + driven by a deterministic flow between random jump times, with a transition…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
The Bou\'e-Dupuis variational formula gives a representation for log Laplace transforms of bounded measurable functions of a finite dimensional Brownian motion on a compact time interval as an infimum of a suitable cost over a collection of…
We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely…
Forecasting complex vehicle and pedestrian multi-modal distributions requires powerful probabilistic approaches. Normalizing flows (NF) have recently emerged as an attractive tool to model such distributions. However, a key drawback is that…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Trajectory optimization (TO) is an efficient tool to generate a redundant manipulator's joint trajectory following a 6-dimensional Cartesian path. The optimization performance largely depends on the quality of initial trajectories. However,…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
In this paper, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes…