Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 26216975.
- Also identified by DOI 10.1073/pnas.1512080112 and PMC identifier 4538664.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
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 we consider time-dependent problems and introduce a fully discrete solution method, 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.