Difference between revisions of "SciML curriculum"
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== 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 === | ||
| Line 45: | Line 45: | ||
** 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 | ||
| − | |||
== Finite Differences == | == Finite Differences == | ||
Revision as of 19:29, 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
- 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, Worksheets 7, 8. Particularly the charged particle one
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
Finite Differences
Reading materials
- 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
Exercises
TUM SciComp1, Worksheet 9.
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