Difference between revisions of "SciML curriculum"

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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
  
  
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=== 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, Worksheets 7, 8. Particularly the charged particle one
+
* 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
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* Definition of partial derivative
2D stationary heat equation
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* 2D stationary heat equation
2D diffusion equation
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* 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/]
+
** 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]
+
** 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]
+
** 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 ==
 
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://en.wikipedia.org/wiki/Physics-informed_neural_networks
[https://github.com/tum-pbs/Physics-Based-Deep-Learning]
+
* 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]
+
** 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]
+
** 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]
+
** 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://mitmath.github.io/18337/
** [https://book.sciml.ai/]
+
** 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


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
  • 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

Reading materials

  • TUM SciComp Lecture 5

Finite Differences

Reading materials

  • TUM SciComp, Lecture 5
  • 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

Video lectures

Lecture notes (almost a textbook)


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