Related papers: Rare Event Analysis via Stochastic Optimal Control
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
Understanding mechanisms of rare but important events in complex molecular systems, such as protein folding or ligand (un)binding, requires accurately mapping transition paths from an initial to a final state. The committor is the ideal…
Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that…
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…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as…
We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
Event-triggered control (ETC) is claimed to provide enormous reductions in sampling frequency when compared to periodic sampling, but little is formally known about its generated traffic. This work shows that ETC can exhibit very complex,…
Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare…
Trajectory planning for autonomous driving is challenging because the unknown future motion of traffic participants must be accounted for, yielding large uncertainty. Stochastic Model Predictive Control (SMPC)-based planners provide…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
We consider control of reaction and population systems by deterministically imposed transitions between the states with different numbers of particles or individuals. Even where the imposed transitions are significantly less frequent than…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
We demonstrate that Optimal Control Theory (OCT) with a state-dependent constraint which depends on the state of the system at each instant can reproduce the famous counterintuitive mechanism of Stimulated Raman adiabatic passage (STIRAP).…
Self-triggered control (STC) and periodic event-triggered control (PETC) are aperiodic sampling techniques aiming at reducing control data communication when compared to periodic sampling. In both techniques, the effects of measurement…
Determining the kinetic bottlenecks that make transitions between metastable states difficult is key to understanding important physical problems like crystallization, chemical reactions, or protein folding. In all these phenomena, the…
Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low…