FY553: The dark universe and (neural) networks

Students taking the course are expected to:

• Have knowledge of classical mechanics and basic knowledge of special relativity, but there are no further prerequisites.
• [Optional] Basic differential calculus and fundamental skills of Python.
  

Our universe presents us with a tantalizing riddle, namely to understand the structure of its "dark sector". This sector includes the dark matter, which could be a new particle and/or black holes. The course will provide an introduction to the topic of dark matter as a whole and discuss some candidates.

In the second part, the course links to the topic of neural networks, which are becoming powerful tools to tackle deep questions in fundamental physics, including the structure of the dark sector. Finally, networks show up in the fundamental physics of the universe in a different way, namely as a proposal for the deep structure of spacetime itself.
 
This course will link a theoretical overview of some of the most exciting questions in fundamental physics with applications that bridge the gap to computer science and is suitable for students with a range of different backgrounds in physics (both applied and theoretical), computing and mathematics.

Competences that the students will acquire during the course include:

• Learning methods, both numerical and analytical, to analyze questions in theoretical physics
• Understand central aspects of modern theoretical physics, including questions in astrophysics and the structure of spacetime.
  

• Give the competence to understand complex problems and devise strategies to tackle them.
  
• Give skills to solve questions in theoretical physics.
  
• Give knowledge and understanding of basic statistics.
  
• Give knowledge and understanding of neural networks and their application, in particular with dark matter physics.
• Give knowledge and understanding of aspects of special relativity.
  

• Understand how causality translates into a network-structure for spacetime, which provides an in-depth understanding of special relativity.
• Understand the basics of the mathematics of partial orders.
  
• Apply both numerical and analytical tools to construct and analyze networks.
  
• Apply both frequentist inference and Bayesian inference to simple regression problems.
• Demonstrate knowledge of the basic evidence for dark matter in astronomical data 
• Construct simple neural networks and apply them to classification of regression problems in the context of DM physics.

• Causality and causal structure of spacetime.
• Basics of partial orders and their relations to networks.
  
• Concept of frequentist inference and Bayesian inference and neural networks.
• Dark Matter astrophysics

• Intro phase: 18 hours
• Skills training phase: 18 hours, hereof tutorials: 10 hours and programming and data analysis exercises: 8 hours

• Solution of an elected project in the topics of the course