Combining Partial Differential Equations, Machine Learning and Measurements for Increased Prediction Capability
Number of credits: 3 hp
Where:
Linköping University, Department of Mathematics
Schedule:
16-20 September 2019, 5 full days.
Examiner:
Jan Nordström
Course literature: Lecture notes and reference to relevant articles.
Lecture notes and reference to relevant articles.
Course contents:
- General principles and ideas. The energy method. Semi-bounded operators. Symmetric and skew-symmetric operators. Well-posed boundary conditions. The error equation.
- Boundary treatments. Summation by parts (SBP) operators. Weak boundary conditions. Time-integration and fully discrete stability.
- Using artificial neural networks (ANNs) in combination with PDEs for increased prediction capability. Stability and accuracy considerations.
- Using experimental results (ER) in combination with PDEs for increased prediction capability. Stability and accuracy considerations.
- Using ANNs and ER in combination with PDEs for increased prediction capability. Stability and accuracy considerations.
Organisation:
Before the course: 1 week of study on material that I send out.
During the course: 5 Lectures, 3 exercises, 2 seminars. Approximately 15 hours.
After the course: 1 week of work with homework
Examination: 3 mandatory HWs.
Prerequisites:
Good general knowledge in: calculus, integrals, differentiation, Fourier-transforms, linear algebra, functional analysis, programming.
Application
This course is sponsored by eScience collaboration initiative.