Difference between revisions of "SciML curriculum"

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** https://people.maths.ox.ac.uk/trefethen/1all.pdf
 
** https://people.maths.ox.ac.uk/trefethen/1all.pdf
 
** Chapter 1, sections 2,3
 
** Chapter 1, sections 2,3
 +
 +
* Iserles, Numerical Analysis of Differential Equations
 +
** Chapters 1,2 (maybe some of chapter 3)
  
 
=== Exercises ===
 
=== Exercises ===
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** https://people.maths.ox.ac.uk/trefethen/3all.pdf
 
** https://people.maths.ox.ac.uk/trefethen/3all.pdf
 
** 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 ==

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