Related papers: Slow manifold and parameter estimation for a nonlo…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
This paper proposes an algorithm that combines Fast Moving Horizon Parameter Estimation and Model Predictive Control subject to an observability constraint designed to ensure a lower bound on the performance of the parameter estimator.…
This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…
Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a…
We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…