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=== Video lectures === | === Video lectures === | ||
| − | https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-1-the-geometrical-view-of-y-f-x-y/ | + | * https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-1-the-geometrical-view-of-y-f-x-y/ |
=== Reading materials === | === Reading materials === | ||
| − | 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/1all.pdf | + | ** https://people.maths.ox.ac.uk/trefethen/1all.pdf |
| − | Chapter 1, sections 1 | + | ** Chapter 1, sections 1 |
| Line 16: | Line 16: | ||
=== Video lectures === | === Video lectures === | ||
| − | https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-2-eulers-numerical-method-for-y-f-x-y/ | + | * https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-2-eulers-numerical-method-for-y-f-x-y/ |
=== Reading materials === | === Reading materials === | ||
| − | Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations | + | * 16.90 Lecture notes |
| − | https://people.maths.ox.ac.uk/trefethen/1all.pdf | + | ** Lecture 1: Numerical Integration of Ordinary Differential Equations |
| − | Chapter 1, sections 2,3 | + | ** 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 | ||
| + | |||
| + | * Iserles, Numerical Analysis of Differential Equations | ||
| + | ** Chapters 1,2 (maybe some of chapter 3) | ||
=== Exercises === | === Exercises === | ||
| − | TUM SciComp 1, | + | * TUM SciComp 1, Worksheet 6. Exercises 3,4 |
| − | + | * TUM SciComp 1, Worksheet 7. Exercise 1,2,3 | |
== Brief Introduction to Partial Differential Equations == | == Brief Introduction to Partial Differential Equations == | ||
| − | Definition of partial derivative | + | * Definition of partial derivative |
| − | 2D stationary heat equation | + | * 2D stationary heat equation |
| − | 2D diffusion equation | + | * 2D diffusion equation |
=== Video lectures === | === Video lectures === | ||
* MIT 18.02 introduction to partial derivatives | * MIT 18.02 introduction to partial derivatives | ||
| − | ** | + | ** https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007/resources/lecture-8-partial-derivatives/ |
=== Reading materials === | === Reading materials === | ||
* Trefethen: The (Unfinished) PDE coffee table book: Description of the heat equation | * Trefethen: The (Unfinished) PDE coffee table book: Description of the heat equation | ||
| − | ** | + | ** https://people.maths.ox.ac.uk/trefethen/pdectb/heat2.pdf |
* Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations | * Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations | ||
| Line 46: | Line 53: | ||
** Chapter 3, section 1 | ** Chapter 3, section 1 | ||
| + | * TUM SciComp Lecture 5 | ||
== Finite Differences == | == Finite Differences == | ||
=== 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 |
| − | ** 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 == | |
Interested in convolutional neural nets | Interested in convolutional neural nets | ||
== Physics-informed 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 === | === Video lectures === | ||
* Differentiable Physics for Deep Learning, Overview Talk by Nils Thuerey | * Differentiable Physics for Deep Learning, Overview Talk by Nils Thuerey | ||
| − | ** | + | ** https://www.youtube.com/watch?v=BwuRTpTR2Rg |
* Partial Differential Equations (PDEs), Convolutions, and the Mathematics of Locality | * Partial Differential Equations (PDEs), Convolutions, and the Mathematics of Locality | ||
| − | ** | + | ** https://www.youtube.com/watch?v=apkyk8n0vBo |
* Mixing Differential Equations and Neural Networks for Physics-Informed Learning | * Mixing Differential Equations and Neural Networks for Physics-Informed Learning | ||
** https://book.sciml.ai/notes/15/ | ** https://book.sciml.ai/notes/15/ | ||
| − | ** | + | ** https://www.youtube.com/watch?v=YuaVXt--gAA |
=== Lecture notes (almost a textbook) === | === Lecture notes (almost a textbook) === | ||
| − | The above two video lectures are from a grad-level course on SciML: | + | * The above two video lectures are from a grad-level course on SciML: |
| − | ** | + | ** https://mitmath.github.io/18337/ |
| − | ** | + | ** https://book.sciml.ai/ |
Latest revision as of 19:50, 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
- Iserles, Numerical Analysis of Differential Equations
- Chapters 1,2 (maybe some of chapter 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