SciML curriculum

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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

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

Exercises

TUM SciComp1, Worksheet 9.


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