NG33A-1865
A discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics
Wednesday, 16 December 2015
Poster Hall (Moscone South)
Fei Lu, Lawrence Berkeley National Laboratory, Berkeley, CA, United States; University of California Berkeley, Mathematics, Berkeley, CA, United States and Alexandre J Chorin, University of California Berkeley, Berkeley, CA, United States
Abstract:
Prediction for a high-dimensional nonlinear dynamic system often encounters difficulties: the system may be too complicated to solve in full, and initial data may be missing because only a small subset of variables is observed. However, only a small subset of the variables may be of interest and need to be predicted. We present a solution by developing a discrete stochastic reduced system for the variables of interest, in which one formulates discrete solvable approximate equations for these variables and uses data and statistical methods to account for the impact of the other variables. The stochastic reduced system can capture the long-time statistical properties of the full system as well as the short-time dynamics, and hence make reliable predictions. A key ingredient in the construction of the stochastic reduced system is a discrete-time stochastic parametrization based on the NARMAX (nonlinear autoregression moving average with exogenous input) model. As an example, this construction is applied to the Lorenz 96 system.
