Neural Networks - Data-Driven Dynamics | Lecture 18

Universal approximation theorems provide the theoretical underpinning for neural networks and machine learning in general. In this lecture we demonstrate how to lift theory to the computational setting. In particular, we go through the basic structure of a neural network on the computer and discuss training it using gradient descent. We further discuss backpropagation for speeding up the training by passing re-used information backward through the network during the gradient descent updating step. The lecture concludes with a simple MATLAB demonstration that builds a neural network by hand and trains it using backpropagation.

Coding demonstration in MATLAB comes from neural_network.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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