Abstract:
Fine-scale models based on high-dimensional differential equations (DEs) are available for many systems in science and engineering. In many cases, research focuses on effects which occur on a coarser scale instead of the fine one described by the DEs. As it is usually not feasible to observe coarse phenomena by direct integration of the fine-scale models at hand, the goal is to find coarser grained descriptions which capture the salient features of the system. In this thesis, we propose a method to automatically extract such a coarse-scale predictive model when fine-scale data of a system is provided.