Chaos Theory and Machine Learning
Name Surname
Dept. name of organization
(of Affiliation)
Name of organization
(of Affiliation)
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email address or ORCID
Abstract- The coming of machine learning However, the coming of machine learning
changes this view of chaos theory. In changes this view of chaos theory. Scientists
chaos theory, relatively complex behavior have used machine learning to revolutionize
can be mapped using dynamic and non- the outcome of a chaotic systems [1]. In
linear systems. This paper explores the chaos theory, relatively complex behavior
relationship between dynamical system can be mapped using dynamic and non-
theory, chaotic system and machine linear systems. Chaos theory can be defined
learning. within four different model, the correlation
dimension, False Nearest Neighbour, phase
Keywords- Chaos theory, machine
space reconstruction and Mutual
learning, chaotic system.
Information Function [2]. While
According to chaos theory, the butterfly predications can be made using machine
effect makes it impossible to make long- algorithms, but can machines actually
term prediction of events. It noted that a understand the systems that they seek to
small change in the path causes a widescale predict. Prediction and understanding are
perturbation to the system resulting into a different concepts in sciences, however,
dramatic change in the predicted path. Thus, machines can use historical data develop a
chaos theory noted that the disturbance statistical understanding of a system
make complicates a system in away that intended to be predicted [2]. In chaos theory,
makes prediction highly uncertain. the combination possible alternatives can be
, analyzed and reduced to the most probable traditional models of historical prediction,
outcome. Chaos theory is based on the this extended to twelve Lyapunov prediction
probability of reducing the butterfly effect in [5]. The integration of the models shows that
predication of phenomenon where the range machine learning is overcoming previous
of outcome are indefinite. limitation in predication of chaotic systems.
Research by Ed Ott and colleagues In Green & Lavesson, a relationship
employed machine learning algorithm called between dynamical system theory and
reservoir to map the progression of chaotic chaotic system is further explored [6]. The
systems; the turbulence and spatiotemporal researchers combined the understanding of
chaos, the Kuramoto-Sivashinsky equation. dynamical system and data-driven model
By training the algorithm, with historical complex systems. Without the inclusion of
data, the researchers were able to predict machine learning, the researchers concluded
eight Lyapunov iteration of the future, this that statistical modelling does not provide
was eight steps deeper into the predication accurate predication of the chaotic systems.
than previously done [3]. The Lyapunov is a In Harikrishnan & Nagaraj, the
measure of the time its takes for a two researcher solved chaotic three-body
nearly identical chaotic systems to show problems of a neural network [7]. The study
divergence. Thus, Lyapunov is a measure of trained neural network so that the network
predictability of a chaotic system [4]. The can predict trajectories much ahead of
results posits that accurate predication could previous capabilities. Three-body analysis is
be made by using only data. However, one of the primary chaotic problem
developing a working machine algorithm proposed by Newton; it involves solving
relies on the accuracy of data in relation to motion equations of three bodies acted upon
the possible outcomes. their own gravitational forces. Three-body
A research published by Sparrow) motion is a classical chaos problem in
further developed the understanding of physics following Poincar attracted attention
chaos theory, predication of chaotic systems to the non-integrability and chaotic nature of
such as the Kuramoto-Sivashinsky equation the phenomenon [4]. By using arbitrary
became more accurate with hybridization of numerical integration, deep artificial neural
data-controlled machine learning and networks provide an accessible solution to
Name Surname
Dept. name of organization
(of Affiliation)
Name of organization
(of Affiliation)
City, Country
email address or ORCID
Abstract- The coming of machine learning However, the coming of machine learning
changes this view of chaos theory. In changes this view of chaos theory. Scientists
chaos theory, relatively complex behavior have used machine learning to revolutionize
can be mapped using dynamic and non- the outcome of a chaotic systems [1]. In
linear systems. This paper explores the chaos theory, relatively complex behavior
relationship between dynamical system can be mapped using dynamic and non-
theory, chaotic system and machine linear systems. Chaos theory can be defined
learning. within four different model, the correlation
dimension, False Nearest Neighbour, phase
Keywords- Chaos theory, machine
space reconstruction and Mutual
learning, chaotic system.
Information Function [2]. While
According to chaos theory, the butterfly predications can be made using machine
effect makes it impossible to make long- algorithms, but can machines actually
term prediction of events. It noted that a understand the systems that they seek to
small change in the path causes a widescale predict. Prediction and understanding are
perturbation to the system resulting into a different concepts in sciences, however,
dramatic change in the predicted path. Thus, machines can use historical data develop a
chaos theory noted that the disturbance statistical understanding of a system
make complicates a system in away that intended to be predicted [2]. In chaos theory,
makes prediction highly uncertain. the combination possible alternatives can be
, analyzed and reduced to the most probable traditional models of historical prediction,
outcome. Chaos theory is based on the this extended to twelve Lyapunov prediction
probability of reducing the butterfly effect in [5]. The integration of the models shows that
predication of phenomenon where the range machine learning is overcoming previous
of outcome are indefinite. limitation in predication of chaotic systems.
Research by Ed Ott and colleagues In Green & Lavesson, a relationship
employed machine learning algorithm called between dynamical system theory and
reservoir to map the progression of chaotic chaotic system is further explored [6]. The
systems; the turbulence and spatiotemporal researchers combined the understanding of
chaos, the Kuramoto-Sivashinsky equation. dynamical system and data-driven model
By training the algorithm, with historical complex systems. Without the inclusion of
data, the researchers were able to predict machine learning, the researchers concluded
eight Lyapunov iteration of the future, this that statistical modelling does not provide
was eight steps deeper into the predication accurate predication of the chaotic systems.
than previously done [3]. The Lyapunov is a In Harikrishnan & Nagaraj, the
measure of the time its takes for a two researcher solved chaotic three-body
nearly identical chaotic systems to show problems of a neural network [7]. The study
divergence. Thus, Lyapunov is a measure of trained neural network so that the network
predictability of a chaotic system [4]. The can predict trajectories much ahead of
results posits that accurate predication could previous capabilities. Three-body analysis is
be made by using only data. However, one of the primary chaotic problem
developing a working machine algorithm proposed by Newton; it involves solving
relies on the accuracy of data in relation to motion equations of three bodies acted upon
the possible outcomes. their own gravitational forces. Three-body
A research published by Sparrow) motion is a classical chaos problem in
further developed the understanding of physics following Poincar attracted attention
chaos theory, predication of chaotic systems to the non-integrability and chaotic nature of
such as the Kuramoto-Sivashinsky equation the phenomenon [4]. By using arbitrary
became more accurate with hybridization of numerical integration, deep artificial neural
data-controlled machine learning and networks provide an accessible solution to
