Related papers: Doob's Lagrangian: A Sample-Efficient Variational …
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…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path…
Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic…
An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…
The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…
A numerical simulation method, based on Dang et al.'s self-consistent theory of large-amplitude collective motion, for rare transition events is presented. The method provides a one-dimensional pathway without knowledge of the final…
The committor functions are central to investigating rare but important events in molecular simulations. It is known that computing the committor function suffers from the curse of dimensionality. Recently, using neural networks to estimate…
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…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a non-linear drift. The latter appears naturally when applying…
Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
We propose here some new sampling algorithms for Path Sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called…
This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable.…
Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO problem to generate robust motions can easily lead to an…