Model Discovery with Autoencoders - Data-Driven Dynamics | Lecture 27

In this final lecture of the series, we explore the cutting-edge use of autoencoders to learn and analyze the dynamics of complex systems. Autoencoders are shown to not only perform dimensionality reduction but also to intelligently warp the data, revealing low-dimensional structures that optimally capture the system’s behavior. We demonstrate these ideas with chaotic Poincaré map data from the Rössler and Gissinger systems, highlighting how autoencoders can uncover hidden order within chaos. In both examples, we see their remarkable potential to forecast system behavior and extract critical information, including the identification of unstable periodic orbits that densely populate the chaotic attractor. This lecture showcases how modern machine learning tools can bridge data-driven approaches and classical dynamical systems theory, offering a powerful framework for understanding and predicting complex phenomena. See my original paper where much of this comes from: https://www.sciencedirect.com/science... Jupyter notebook comes from Rossler_conj.ipynb and Gissinger_conj.ipynb here: https://github.com/jbramburger/DataDr... PyTorch version: https://github.com/jbramburger/DataDr... Get the book here: https://epubs.siam.org/doi/10.1137/1.... Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDr... 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.