Use of machine learning to forecast the behaviour of chaotic dynamical systems

Research project would involve mathematical modelling, computer simulations and machine learning.
Initial idea is to use machine learning to forecast the behaviour of chaotic dynamical systems.
Chaotic dynamic appears in many natural systems, ranging from physical and biological to weather
and climate applications. It can be studied by mathematical models that generate deterministic
chaos. Chaotic systems are sensitive to the initial conditions, which makes them difficult to
predict. Sensitivity is quantified by Lyapunov exponents that in most cases must be found using
numerical techniques. Recently it was suggested [1,2] to use deep learning artificial neural
networks (ANN) for forecasting in such systems.
Deep learning algorithms can be trained to predict the future behaviour of chaotic systems [1,2].
They can also be taught to recognise chaotic behaviour [4]. Prediction and recognition could also
be used with fractals to see if ANN can continue/reproduce fractals or recognise fractal patterns
from input image or time-series data.
The aim of the project would be to extend such a direction further by studying
fractal artificial intelligence (AI) [3] and related algorithms ability to recognise chaos or
fractal patterns. I would also like to consider some of the (AI) research topics listed
in [3] - distributed computing, learning capabilities and real-time decision-making. Topics of
consciousness or universality are also intriguing.
Methodology and Programming Languages: The mathematical component will be built upon my
existing educational background and knowledge of chaotic dynamical systems I have acquired in the
last two years working on my FYP and MMath projects. Different programming languages would be
considered based on the direction that the project takes. Python would be a good language to use,
but it would take some time to learn. Another option is to use MATLAB as newer versions provide
tools to study deep learning, and I have almost 4 years of experience with the
program. Other languages can also be used, as appropriated for the task.
Draft plan is to start by studying the existing machine learning algorithms, focusing on deep
learning (ANN) and fractal AI. Later the research would shift to forecasting and/or further work on
more specific research topics (AI). A Restricted three-body problem will be initially
used to benchmark the methodology, but this will be expanded in due course to incorporate other
types of dynamical systems as well.