Modul

The module will be completed by an oral exam (about 30 min).

The goal of the lecture is to provide a mathematical foundation of neural networks from the perspective of numerical analysis. Students know basic definitions and terminology as well as classical approximation results for neural networks. They are familiar with numerical methods for the efficient training of neural networks and can analyze them. Moreover, students can apply the concepts to popular applications in the context of partial differential equations (such as physics-informed neural networks).

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• Neural networks
• Approximation results
• Connections to finite element methods
• Numerical methods for the efficient learning
• Physics-informed neural networks

A solid background in numerical mathematics is strongly recommended. Basic knowledge of functional analysis and finite element methods is helpful, but not required.

Total workload: 180 hours

Attendance: 60 h

• lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination