Model Reduction in Classical Molecular Dynamics

Abstract

This thesis explores different routes to model reduction in the context of classical molecular dynamics. Adopting a reductionist's point of view, our main concern is the sound causal explanation of observable macroscopic properties, e.g., activation energies or dynamical stability of conformations in terms of the microscopic physical model. Notwithstanding computational aspects, the difficulty lies in the sheer complexity of the microscopic models with their vastly different spatial and temporal scales. Roughly speaking, reduced modelling comes in two varieties: elimination of specific (e.g., fast) degrees of freedom from the original model, or parametrization of certain simplified models. The first approach is usually referred to as "mode reduction", whereas the latter is often termed "remodelling". In this thesis we mainly focus on mode reduction, since sticking to the original microscopic model means to keep as much of the problem's physics as possible. (The microscopic models are based on profound physical and chemical knowledge, both theoretical considerations and experimental data, which constitutes their empirical adequacy and predictive power.) In doing so, we extend and refine available methods of mode reduction such as averaging or projection operator techniques and set them in context with one another. Nevertheless we also allude to aspects of parametrized models.