Code
Φ-842
Level
Graduate
Category
B
Teacher
G. Tsironis
ECTS
5
Hours
4
Semester
Spring
Display
Yes
Offered
Yes
Teacher Webpage
Goal of the course
The course introduces methods of Artificial Intelligence (AI) and in particular Machine Learning (ML) in Complex Dynamical Systems. The aim is two-fold; on one hand it presents a very basic introduction to ML while, on the other hand, it uses the ML methods in the study of Complex systems. Prerequisites include basic computational tools and knowledge of classical and quantum mechanics. Expected outcomes: Knowledge of ML and Complex Systems and practical use of various ML techniques.
Program
Monday, 15:00-17:00, 2st floor semminar room
Thursday, 9:00-11:00, 2st floor semminar room
Thursday, 9:00-11:00, 2st floor semminar room
Syllabus
Brief introduction to Machine Learning, types of ML, standard methods of regression, support vector machines, trees and forests, artificial neural networks.
Introduction to basic concepts of nonlinear dynamical systems, differentiation between integrable and non-integrable systems, focus on the Discrete Nonlinear Schrödinger (DNLS) equation. Analytical solutions through elliptic functions, spectral properties and basic features of dynamics.
Focus on integrable DNLS equation units and apply ML in order to extract known analytical results such as the self-trapping transition and the Targeted Energy Transfer (TET) condition for a two unit system. Use ML methods for non-integrable DNLS units.
Chaotic systems, nonlinear time series analysis, embedding dimension. Extraction of dynamical system properties from the time series. Application of ML in chaotic time series, autoencoders, latent space dimensionality.
Comparison of various ML methods when applied in dynamical systems. Feed forward neural networks, LSTM, reservoir computing. Extraction of coherence in spatiotemporal dynamics.
Physics Informed Machine Learning (PIML), application in real data. The SIR model of epidemiology, application to COVID-19. Biomedical applications of ML and PIML.
Introduction to basic concepts of nonlinear dynamical systems, differentiation between integrable and non-integrable systems, focus on the Discrete Nonlinear Schrödinger (DNLS) equation. Analytical solutions through elliptic functions, spectral properties and basic features of dynamics.
Focus on integrable DNLS equation units and apply ML in order to extract known analytical results such as the self-trapping transition and the Targeted Energy Transfer (TET) condition for a two unit system. Use ML methods for non-integrable DNLS units.
Chaotic systems, nonlinear time series analysis, embedding dimension. Extraction of dynamical system properties from the time series. Application of ML in chaotic time series, autoencoders, latent space dimensionality.
Comparison of various ML methods when applied in dynamical systems. Feed forward neural networks, LSTM, reservoir computing. Extraction of coherence in spatiotemporal dynamics.
Physics Informed Machine Learning (PIML), application in real data. The SIR model of epidemiology, application to COVID-19. Biomedical applications of ML and PIML.
Bibliography
1. Notes of G. Tsironis
2. A. Geron, Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow 3e : Concepts, Tools, and Techniques to Build Intelligent Systems (O’ Reilly 2022)
3. H. Abarbanel, Analysis of Observed Chaotic Data (Springer 1997)
4. V. M. Kenkre, Interplay of Quantum Mechanics with Nonlinearity (Springer 2022)
2. A. Geron, Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow 3e : Concepts, Tools, and Techniques to Build Intelligent Systems (O’ Reilly 2022)
3. H. Abarbanel, Analysis of Observed Chaotic Data (Springer 1997)
4. V. M. Kenkre, Interplay of Quantum Mechanics with Nonlinearity (Springer 2022)
