A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
نویسنده
چکیده
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper the problem is considered in a fully discrete-time setting, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori-Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system.
منابع مشابه
On the Design of Nonlinear Discrete-Time Adaptive Controller for damaged Airplane
airplane in presence of asymmetric left-wing damaged. Variations of the aerodynamic parameters, mass and moments of inertia, and the center of gravity due to damage are all considered in the nonlinear mathematical modeling. The proposed discrete-time nonlinear MRAC algorithm applies the recursive least square (RLS) algorithm as a parameter estimator as well as the error between the real ...
متن کاملDeveloping a 3D stochastic discrete fracture network model for hydraulic analyses
Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...
متن کاملA Discrete Stochastic Approach to Hotel Revenue Management
A linear programming model has been presented for finding an appropriate planning in order to maximize hotel revenue. In this model, a special planning horizon has been considered that includes several busy days of a year. There are several reservation periods that may start a few months earlier. Each period of reservation may have different prices and so result different incomes. Hotel custo...
متن کاملDiscrete Hessian Eigenmaps method for dimensionality reduction
For a given set of data points lying on a low-dimensional manifold embedded in a high-dimensional space, the dimensionality reduction is to recover a low-dimensional parametrization from the data set. The recently developed Hessian Eigenmaps is a mathematically rigorous method that also sets a theoretical framework for the nonlinear dimensionality reduction problem. In this paper, we develop a ...
متن کاملDiscrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics.
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. ...
متن کامل