Dynamic Mode Decomposition - Data-Driven Dynamics | Lecture 3

In this lecture we present dynamic mode decomposition (DMD). DMD is a powerful method for both forecasting and interpreting nonlinear datasets using a simple and efficient algorithm. We begin by outlining the method in theory and then implementing it in MATLAB to see what we can find. Along the way we draw attention to the similarities and differences between it and proper orthogonal decomposition. We further improve the method by considering physics-informed DMD (piDMD) which augments DMD by incorporating known physics into the algorithm. In the demonstration to the nonlinear Schrodinger equation presented in this video lecture, this means assuring that the number of particles is conserved in the quantum system as we progress through time. Coding demonstration in MATLAB comes from DMD_Schrodinger.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Linear%20Evolution%20Models For a great demonstration of both POD and DMD to fluid flow, check out this link: https://levelup.gitconnected.com/demystify-fluid-flow-with-dynamic-mode-decomposition-dmd-1da54c805ed6 Get the book here: https://epubs.siam.org/doi/10.1137/1.9781611978162 Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDrivenDynSyst This book provides readers with: - methods not found in other texts as well as novel ones developed just for this book; - an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities; - examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and - a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.