Related papers: Dynamic maximum entropy provides accurate approxim…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a…
We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in deterministic cases when the possible…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
Snapshot back-ended reduced basis methods for dynamical systems commonly rely on the singular value decomposition of a matrix whose columns are high-fidelity solution vectors. An alternative basis generation framework is developed here. The…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low dimensional descriptions from high dimensional observations. However, existing…
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…
Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution.…
Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
We present a control framework for stochastic compartmental models in epidemiology. In this framework, rather than directly controlling the stochastic system, we perform optimal control of an associated Fokker-Planck equation, with the goal…
We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the {\em special endogenous solution} to a stochastic fixed-point…