Han Cheng Lie & Gottfried Hastermann, Freie Universität Berlin
"What is ... data assimilation and nonequilibrium Monte Carlo rare event sampling for multiscale dynamical systems?"
The complexity of multiscale dynamical systems often calls for probabilistic or statistical approaches. For example, given a set of observations of a dynamical system, one may wish to forecast its behavior up to some time in the future. Such methods are called `data assimilation methods'. We shall present a basic data assimilation method and illustrate some problems that can arise when one applies data assimilation methods to study multiscale dynamical systems, using the simple and informative model of the double pendulum.
Alternatively, when one wishes to study a system that has explicitly random dynamics, one may face the problem that sampling from the true probability distribution of interest using simple Monte Carlo is too inefficient to be practical. This is often the case when the distribution of interest involves a rare event. We will present metastable overdamped Langevin diffusions as a class of examples that exhibit this property, and discuss a general solution strategy involving alternative probability distributions.
These two talks shall cover some of the basic ideas of SFB Projects A02 and A05.