Optimal Prediction in Molecular Dynamics

Optimal prediction is a method to approximate the average solution of a large system of ordinary differential equations by a smaller system. In this thesis we show how optimal prediction can be applied in the field of molecular dynamics in order to reduce the number of particles. We apply optimal prediction to a model problem describing a surface coating process and show how asymptotic methods can be used to approximate the original system by a smaller system. We consider the reduction of computational effort and analyze – analytically and by numerical experiments – under which conditions the optimal prediction system is a valid approximation to the original system.