Related papers: A new stochastic mode reduction strategy for dissi…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We examine the problem of predicting the evolution of solutions of the Kuramoto-Sivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations…
A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
We are concerned with quasilinear symmetrizable partially dissipative hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following our recent work [10] dedicated to the one-dimensional case, we establish the existence of…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…