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Identifier 000425748
Title Predicting dynamical chaos with recurrent neural networks
Alternative Title Προβλέποντας δυναμικό χάος με επανατροφοδοτούμενα νευρωνικά δίκτυα
Author Βίλλια, Μαρία Μυρτώ Χ.
Thesis advisor Τσιρώνης, Γεώργιος
Abstract Predicting chaotic phenomena is tempting. And how could it not be when the most common definition of chaos is unpredictability? In the present study we are attempting to predict chaotic time series. These time series are produced by two models that can appear chaotic behaviour; namely the Lorenz and the Hindmarsh-Rose models. In order to succeed it, we use a machine learning algorithm called Long Short Term Memory (LSTM). In particular, in Chapter 1 we present the two used chaotic models, we give the definitions of some basic concepts of chaos, and we provide in detail the aims of this work. Then, in Chapter 2, we introduce the basic theory of artificial neural networks and we focus on the recurrent neural networks, where the LSTMs algorithms are a special category. Finally, in Chapter 3 we present our results and in Chapter 4 their discussion. Analytically, in Chapter 3 we initially study three specific time series produced by the Lorenz model. The results of our simulations show that there is a clear relationship between their prediction horizon and their Lyapunov exponents. At the same time we demonstrate that this relationship although it is not evident, it depends on the number of training data. Finally, in the same Chapter 3 we demonstrate a variant of our main method which provides better predictions on extreme chaotic time series. Obviously, experimenting with chaos is certainly not an easy task. We need to develop advanced programming and try out many different versions of our algorithm before reaching our goals. In this context, we study a time series with peculiar behavior produced by the Hindmarsh-Rose model and we present our most interesting results.
Language English
Subject Machine learning
Μηχανική μάθηση
Issue date 2019-11-29
Collection   Faculty/Department--Faculty of Sciences and Engineering--Department of Physics--Post-graduate theses
  Type of Work--Post-graduate theses
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