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Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order…
This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…
Labeled transition systems are typically used to represent the behavior of nondeterministic processes, with labeled transitions defining a one-step state to-state reachability relation. This model has been recently made more general by…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Temperature-accelerated sliced sampling (TASS) is a well-established enhanced sampling method that facilitates exhaustive exploration of high-dimensional collective variable (CV) space through directed sampling employing a combination of…
Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…