Related papers: Stochastic Optimal Prediction for the Kuramoto-Siv…
The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate…
In this article we study the solution of the Kuramoto-Sivashinsky equation (for surface erosion or surface growth) on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time…
In this study, approximate solution of Kuramoto-Sivashinsky Equation, by the reduced differential transform method, are presented. We apply this method to an example. Thus, we have obtained numerical solution Kuramoto-Sivashinsky equation.…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
We investigate a fully discrete finite element approximation for the stochastic Kuramoto-Sivashinsky equation, combining the standard finite element methods in spatial discretization with the implicit Euler-Maruyama scheme in time. Rigorous…
Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…
The problem of controlling and stabilising solutions to the Kuramoto-Sivashinsky equation is studied in this paper. We consider a generalised form of the equation in which the effects of an electric field and dispersion are included. Both…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that in an appropriate probability space, the difference between the average of all solutions that satisfy…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately…
We analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good…
In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…
We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The…
Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…
The aim of this paper is to provide a novel systematic methodology for the design of sampled-data observers for Linear Kuramoto-Sivashinsky systems (LK-S) with non-local outputs. More precisely, we extend the systematic sampled-data…
In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid…