This book serves as a comprehensive introduction to nonlinear complex systems through the application of machine learning methods. Artificial intelligence (AI) has affected the foundations of scientific discovery, and can therefore lend itself to developing a better understanding of the unpredictable nature of complex dynamical systems and to predict their future evolution.

Utilizing Python code, this book teaches and applies machine learning to topics such as chaotic dynamics and time-series analysis, solitons, breathers, chimeras, nonlinear localization, biomolecular dynamics, and wave propagation in the heart. The consistent integration of methods and models allow for readers to develop a necessary intuition on how to handle complexity through AI. This textbook contains a wealth of expository material, code, and example problems to support and organize academic coursework, allowing the technical nature of these areas of study to become highly accessible.

Requiring only a basic background in mathematics and coding in Python, this book is an essential text for a wide array of advanced undergraduate or graduate students in the applied sciences interested in complex systems through the lens of machine learning.

Explores artificial intelligence in relation to a wide array of complex systems Provides an accessible introduction to machine learning with python code for advanced students in the applied sciences Includes numerous models, example code, and problems with solutions

Autorentext

Giorgos Tsironis is Professor of Physics at the Department of Physics of the University of Crete in Greece, affiliated researcher at the Institute of Electronic Structure and Laser of FORTH and also the Director of the Institute of Theoretical and Computational Physics of the University of Crete. He is also visiting faculty in the School of Engineering and Applied Sciences of Harvard University. He obtained his PhD in Theoretical Condensed Matter and Statistical Physics from the University of Rochester in USA in 1987. He was then a postdoctoral associate at the University of California San Diego and the Fermi National Accelerator Laboratory before becoming an assistant professor of Physics at the University of North Texas while also affiliated with the Superconducting Super Collider Laboratory. He joined the Department of Physics of the University of Crete in 1994 as associate professor and became professor in 2000. During his carrier he was long-term visiting faculty in numerous institutions such as University of Barcelona in Spain, Technion in Haifa, Israel, Nazarbayev University in Kazakhstan, Cambridge University in the UK and Harvard University in USA. He has been affiliated with Los Alamos National Laboratory and a frequent visitor of its Center for Nonlinear Studies for many decades.

His research interests are in the areas of condensed matter physics, statistical mechanics, nonlinear physics, complexity, biological physics and metamaterials. In 1997 he was awarded the international Stephanos Pnevmatikos award for his many contributions to nonequilibrium statistical mechanics and the theory of solitons in non-linear lattices, with applications to molecular crystals and biophysics. His recent research focus involves the role of nonlinearities and breathers in superconducting as well as quantum metamataterials. He has published over 200 papers in refereed journals while he (co-)organized a number of international conferences, workshops and advanced summer schools in the area of statistical mechanics and non-linear physics.

In recent year his research and teaching is focusing in the use of artificial intelligence (AI) in complex systems. He established a sequence of two undergraduate courses Introduction to Data Science and Machine Learning that are being taught at the University of Crete and also established a Master program at the Greek Open University on Data Science and Machine Learning. He taught the research course on AI and Complex Dynamical Systems at Harvard and the University of Crete. He has used AI in medical and biological applications, such as cardiology, COVID-19 virus spreading and neurodegenerative diseases, in detecting chimeras in complex, spatiotemporal networks as well as in quantum targeting processes.

Inhalt

Chapter 1. Complex systems and machine learning.- Chapter 2. Regression and Classification.- Chapter 3. Data manipulation techniques.- Chapter 4. Artificial neurons and deep learning.- Chapter 5. Powerful neural network architectures.- Chapter 6. Autoencoders and more.- Chapter 7. The Discrete Nonlinear Schr¨odinger Equation.- Chapter 8. Learning Analytical Solutions.- Chapter 9. The targeted energy transfer model.- Chapter 10. Dynamical embedding with autoencoders.- Chapter 11. Chimeras.- Chapter 12. Branching.- Chapter 13. Discrete breathers.- Chapter 14. Quantum targeted transfer with machine learning.- Chapter 15. Learning quantum systems.- Chapter 16. Action potential propagation in the heart.- Chapter 17. Machine learning cardiology.- Chapter 18. Epidemiology with physics informed machine learning.- Chapter 19. Foundations.- Chapter 20. Computational complexity and the butterfly effect.