Difference between revisions of "SciML curriculum"
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=== Reading materials === | === Reading materials === | ||
| + | |||
| + | * TUM SciComp, Lecture 5 | ||
* Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations | * Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations | ||
** https://people.maths.ox.ac.uk/trefethen/3all.pdf | ** https://people.maths.ox.ac.uk/trefethen/3all.pdf | ||
| − | ** Chapter 3, Section 2 | + | ** Chapter 3, Section 2,3 |
| + | |||
| + | * Iserles, Numerical Analysis of Differential Equations | ||
| + | ** Chapter 16, The Diffusion Equation: Sections 1,3 | ||
| + | |||
=== Exercises === | === Exercises === | ||
| − | TUM SciComp1, Worksheet 9. | + | * TUM SciComp1, Worksheet 9. |
| − | + | * TUM SciComp Lab, Worksheet 4. | |
== Neural nets == | == Neural nets == | ||
Revision as of 19:49, 27 June 2022
Ordinary Differential Equations
Formal definition of ODEs, geometrical view, charged particle in a magnetic field
Video lectures
Reading materials
- Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
- https://people.maths.ox.ac.uk/trefethen/1all.pdf
- Chapter 1, sections 1
Numerical methods for solving ODEs
Explicit Euler, Implicit Euler, Trapezoid Rule, RK4
Video lectures
Reading materials
- 16.90 Lecture notes
- Lecture 1: Numerical Integration of Ordinary Differential Equations
- Lecture 6: Runge-Kutta Methods
- Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
- https://people.maths.ox.ac.uk/trefethen/1all.pdf
- Chapter 1, sections 2,3
Exercises
- TUM SciComp 1, Worksheet 6. Exercises 3,4
- TUM SciComp 1, Worksheet 7. Exercise 1,2,3
Brief Introduction to Partial Differential Equations
- Definition of partial derivative
- 2D stationary heat equation
- 2D diffusion equation
Video lectures
- MIT 18.02 introduction to partial derivatives
Reading materials
- Trefethen: The (Unfinished) PDE coffee table book: Description of the heat equation
- Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
- https://people.maths.ox.ac.uk/trefethen/3all.pdf
- Chapter 3, section 1
- TUM SciComp Lecture 5
Finite Differences
Reading materials
- TUM SciComp, Lecture 5
- Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
- https://people.maths.ox.ac.uk/trefethen/3all.pdf
- Chapter 3, Section 2,3
- Iserles, Numerical Analysis of Differential Equations
- Chapter 16, The Diffusion Equation: Sections 1,3
Exercises
- TUM SciComp1, Worksheet 9.
- TUM SciComp Lab, Worksheet 4.
Neural nets
Interested in convolutional neural nets
Physics-informed neural nets
- https://en.wikipedia.org/wiki/Physics-informed_neural_networks
- https://github.com/tum-pbs/Physics-Based-Deep-Learning
Video lectures
- Differentiable Physics for Deep Learning, Overview Talk by Nils Thuerey
- Partial Differential Equations (PDEs), Convolutions, and the Mathematics of Locality
- Mixing Differential Equations and Neural Networks for Physics-Informed Learning
Lecture notes (almost a textbook)
- The above two video lectures are from a grad-level course on SciML:
Papers
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- An improved data-free surrogate model for solving partial differential equations using deep neural networks
- NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations
- Neural Ordinary Differential Equations