Home » PDEs + ANNs + experiments for increased prediction capability – 2019

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:

  1. General principles and ideas. The energy method. Semi-bounded operators. Symmetric and skew-symmetric operators. Well-posed boundary conditions. The error equation.
  2. Boundary treatments. Summation by parts (SBP) operators. Weak boundary conditions. Time-integration and fully discrete stability.
  3. Using artificial neural networks (ANNs) in combination with PDEs for increased prediction capability. Stability and accuracy considerations.
  4. Using experimental results (ER) in combination with PDEs for increased prediction capability. Stability and accuracy considerations.
  5. 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

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Notes:

This course is sponsored by eScience collaboration initiative.

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