Tensor Network Methods

What it is about

You learn modern methods for efficient approximation of high-dimensional functions (large N-tensors). The focus is on Tensor-Train (TT) approximation: its theory, numerical algorithms and applications. In the end you can analyze and simulate simple multidimensional problems with tensor-network methods.

What you will be able to do

• Understanding CP-rank and TT-rank
• Knowledge of the Border-Rank problem for CP-Approximation
• Understanding the structure of the manifold of TT states and its tangent space
• Familiarity with the DMRG algorithm
• Insights into applications outside of mathematics
• Ability to analyze and simulate simple multivariate problems with tensor-network methods

What the module consists of

• VorlesungIntroduction to concepts and examples, motivation and fundamentals
• Übung/Practice sessionsWeekly exercise sessions to deepen understanding and work on assignments independently

Teaching method

• TafelvorträgeIntroduction to relevant concepts and examples
• Discussion with studentsPromotes understanding and enables independent study of the literature
• Weekly practice sessions with supervisionConsolidation of the material through individual and group work; increasing independence of students
• Provision of typed lecture notesSelf-study and review