Learning Normal Forms - Data-Driven Dynamics | Lecture 24 скачать в хорошем качестве

Learning Normal Forms - Data-Driven Dynamics | Lecture 24

A full understanding of dynamical systems requires exploring bifurcations, the critical transitions where system behavior changes dramatically. Each bifurcation is associated with a normal form, a canonical system that captures its essential dynamics. Crucially, there exists a local conjugacy between a system exhibiting a bifurcation and its normal form, providing a powerful tool for analysis. In this lecture, we investigate this relationship through a saddle-node bifurcation and demonstrate how to learn the conjugacy using an autoencoder neural network. By combining modern machine learning with classical theory, we achieve results that go beyond what can be done with traditional analytical methods, revealing the structure of bifurcations with unprecedented precision. Jupyter notebook comes from NormalForm_sn.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.