Practical Machine Learning + Chaos

A hacker's approach to machine learning in chaos and complexity


It's widely accepted that machine learning (ML) has been inspired largely by methods from statistical physics. As information theory, statistics and physics continue to cross-pollinate, some of the ML models are being lauded by many scientists as groundbreaking and likely to change our understanding of physical principles.

Physicists like to think that all you have to do is say: 'These are the conditions, now what happens next?'

Richard Feynman

We need more experiments embracing and applying the methods of ML. So, this website is built with practical examples in ML applied to chaos and complexity. More importance is given to computational techniques than theory. Join me as I experiment with ML and try to deduce the most important quantifiers using only a limited data set.

Recent Posts

Lorenz Attractor We start with exploring Lorenz differential equations (also known as Lorenz attractor) using Python through examples, look at extremely complicated, aperiodic, non-transient and locally unstable trajectories created by Lorenz attractor. Read more...
publish date 2019-03-29 chaos strange attractor
Poincaré Surface of Section Poincaré surface of section (also referred to as Poincaré section or Poincaré map) is powerful technique extracting fundamental properties from flows in the form of a discrete maps. A trajectory or set of trajectories are sampled periodically, by looking at successive intersections with a plane in the phase space. Read more...
publish date 2019-04-28 phase space strange attractor
Fractal Dimension In the study of dynamical systems there are many quantities that identify as "entropy". Notice that these quantities are not the more commonly known thermodynamic ones, used in Statistical Physics. Rather, they are more like the to the entropies of information theory, which represents information contained within a dataset, or information about the dimensional scaling of a dataset. Based on the definition of the generalized entropy, one can calculate an appropriate dimension. Read more...
publish date 2019-08-17 chaos time series phase space

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Who is Dr. Kaos?

I have a Ph.D. in Chaos & Nonlinear Dynamics, with a passion for data and finding patterns, so I naturally gravitate towards complexity and uncertainty. I am also a tech entrepreneur with multiple successful exits and with spectacular failures too :-). Over the years, I had the good fortune of working with great engineers and scientists who have helped me with my insatiable appetite for learning, coding, and computational experiments. This website is an effort to help others and to give back to the community (in hopes of generating good karma).

For the past few years, I've been managing a team of engineers, working on interesting optimization problems, implementing ML algorithms, and poking at big data.

What can I expect to find here?

Hopefully, useful and practical techniques!

Half a century ago, the pioneers of chaos theory discovered that the “butterfly effect” makes long-term prediction impossible. That was before ML became a commodity in solving difficult engineering problems. In this website, I share my experimentation with ML using time-series data collected from dynamical systems that chaotic behavior. All work is done with a hacker's approach, i.e. more importance is given to delivering results (computational techniques) than to laying out the theoretical framework.

Who is the target audience?

Anyone interested in learning more about chaos, complexity, and ML. That being said, there are some prerequisites: I assume you know Python and you also have basic knowledge of chaos and nonlinear dynamics. If you don't, I recommend the following books to get you started: