Learning the Lorenz System

Before digging into some of the saucy details of dynamical systems theory, I think it is time to introduce at least a bit of machine learning in this blog. The chance came naturally yesterday, as I wanted to learn how to use Jax, which is a sort of improved numpy, with a “functional soul”. I’m not digging into details about the codind part since I’m far for beeing confident with the library and this post will mainly revolve around the conceptual part of the topic. Yet, I will show all the code I used, so that you can follow through and appreciate the functionalities offered by Jax. If you are not confident with the machine learning ideas, you will maybe find some parts of this blogpost a bit mysterious, but you should still be able to follow through as I’ve tried to explain each step (at least at high-level, which is all we need for now).

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The Butterfly Effect

The butterfly effect is the popular concept that “the flap of a butterfly’s wings in Brazil can set off a tornado in Texas”. This idea, which is in fact misunderstood and misrepresented in many occasions, came from the seminal work of Edward Lorenz, which was conducting methereological simulations. In this brief post, I will reproduce its experiment using a basic numpy simulation to show the origin of its incredible discovery.

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Dynamical Systems

In this first post I’ll simply be discussing some basic aspects of my field of study, which lies at the intersection of Dynamical Systems (DS) and Machine Learning. The scope of this post (and presumably, the following ones) is two-fold: on one hand, it will be used to develop the notation that I’m going to use through the blog posts. On the other hand, it’ll be nice way to familiarize with markdown and the blog format, learning the technical aspects and improving scientific writing.

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