Discrete-time approach to stochastic parameterization of chaotic dynamics
Stochastic parametrization methods aim to reduce the cost of simulating high-dimensional dynamical systems by fitting simpler models to the output of fully-resolved computations. They are especially relevant for systems with many degrees of freedom of which only a small subset are of direct interest.
This talk concerns a discrete-time approach to stochastic parametrization due to Chorin and Lu. I will report on a study of their method in the context of a prototypical model of spatiotemporal chaos, the Kuramoto-Sivashinsky equation, and describe some of the dynamical and computational issues that arise. I will also discuss some connections between this method and the Mori-Zwanzig projection operator formalism of nonequilibrium statistical mechanics. This is joint work with Alexandre Chorin and Fei Lu.