Abstract

We consider the task of system identification and simulation via Dynamic Mode Decomposition (DMD) and physics-informed DMD for a simple heat conduction problem. In this regard, we consider the trade-off between data-driven and model-based simulation at the ex-ample of the one-dimensional heat equation. Thereby, we highlight the similarities between dynamic simulation and data-driven modeling. More precisely, we show how physics-informed DMD can be used to learn a data-adaptive finite-difference model and how this relates to the inherent limitations of finite-difference simulation.