Modeling of Equilibrium and Non-Equilibrium Time-Series Data: From Protein Folding to Weather Forecasting

The generalized Langevin equation is a non-Markovian equation of motion for general reaction coordinates and derived by exact projection techniques from the Hamiltonian dynamics of a many-body system, it constitutes a systematic coarse- graining approach. A few applications are discussed: From large-scale molecular- dynamics simulations of fast-folding proteins the friction is shown to have memory with a decay time similar to the folding time, leading to anomalous and drastically modified protein kinetics. In fact, folding times are not dictated by free-energy barriers, as predicted by the Arrhenius law, but rather by the non-Markovian friction. Memory effects are also present for non-equilibrium systems. After removing slow and periodic trends from the data by filtering, the GLE can be used to predict complex phenomena such as weather data at a fraction of the numerical cost of machine-learning methods.