Automated Model Reduction for Complex Systems Exhibiting Metastability

We present a novel method for the identification of the most important metastable states of a system with complicated dynamical behavior from time series information. The novel approach represents the effective dynamics of the full system by a Markov jump process between metastable states, and the dynamics within each of these metastable states by rather simple stochastic differential equations (SDEs). Its algorithmic realization exploits the concept of Hidden Markov Models (HMMs) with output behavior given by SDEs. The numerical effort of the method is linear in the length of the given time series, and quadratic in terms of the number of metastable states. The performance of the resulting method is illustrated by numerical tests and by application to molecular dynamics time series of a trialanine molecule.