View source for SciML curriculum

== Ordinary Differential Equations == 
Formal definition of ODEs, geometrical view, charged particle in a magnetic field

=== Video lectures ===
* https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-1-the-geometrical-view-of-y-f-x-y/

=== 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 ===
* https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/resources/lecture-2-eulers-numerical-method-for-y-f-x-y/

=== 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
** https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007/resources/lecture-8-partial-derivatives/

=== Reading materials ===

* 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
** 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
** https://www.youtube.com/watch?v=BwuRTpTR2Rg

* 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
** https://book.sciml.ai/notes/15/
** https://www.youtube.com/watch?v=YuaVXt--gAA

=== Lecture notes (almost a textbook) ===

* The above two video lectures are from a grad-level course on SciML:
** https://mitmath.github.io/18337/
** https://book.sciml.ai/


=== 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