Numerical methods in physics

Description

The objective is to introduce machine learning approaches and numerical methods able to treat various physical questions.

Compétences visées

•    Applying knowledge in physics;

•    Apply methods from mathematics and digital technology;

•    Produce a critical analysis, with hindsight and perspective;

•    Interact with colleagues in physics and other disciplines;

•    Research a physics topic using specialised resources;

•    Communicate in writing and orally, including in English;

•    Respect ethical, professional and environmental principles in the practice of physics.

Syllabus

1. Introduction to machine learning
2. Supervised learning:
3. Classification: support vector machine
4. Classification/regression: decision tree
5. Unsupervised learning:
6. Clustering methods
7. dimensional reduction
8. Unified view of classical methods (FD, FE). Application to Helmholtz equation.
9. Tensor method for large dimensional Schrodinger equation.
10. Neural networks bases methods. Application to Grad-Shafranov PDE
11. Eulerian methods. Applicationt to Radiative transfer
12. Semi-Lagrangian methods. Application to linear Vlasov equation.
13. Introduction to physical and data driven model reduction. Applications to previous PDE.

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