Discovering Conserved Quantities - Data-Driven Dynamics | Lecture 11

A conserved quantity of a differential equation is a scalar function that remains constant along the flow of the equation. In this lecture we present a data-driven method that allows one to discover conserved quantities from data gathered from a system. The method relies on defining a dictionary to expand the conserved quantity in, similar to SINDy and EDMD, and then re-frames the discovery problem as a null space linear algebra problem. The lecture begins with a theoretical introduction to conserved quantities and the method, while then moving to a numerical demonstration using MATLAB.

Coding demonstration in MATLAB comes from conserved_quant.m here: 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/

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