An Incremental Approach to Dynamic Mode Decomposition for Time-Varying Systems with Applications to a Model for Erythropoiesis

Abstract

Dynamic Mode Decomposition (DMD) is a new popular, data driven technique to identify time invariant high dimensional dynamical systems by a reduced linearized model. Throughout this thesis, we will, first of all, introduce the standard DMD framework and the Dynamic Mode Decomposition with control (DMDc). Since many applications underly time-varying dynamics, we also will introduce DMD approaches to identify high dimensional systems underlying low dimensional time-varying dynamics. Here, we will come to an approach of block computation, and thereupon we will finally introduce the Online DMD. Considering the different approaches it will turn out, that there does not exist the perfect approach, instead it is depending on the given data. To analyze the different approaches of numerical performance, we will consider a model of Erythropoiesis. The model is a question of a hyperbolic partial differential equation. Therefore, we will also give a slight overview of numerical solving the resulting equation by introducing an upwind-finite-differences scheme.