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https://github.com/comp-physics/awesome-modeling-simulation

Resources for learning about modeling and simulation
https://github.com/comp-physics/awesome-modeling-simulation

List: awesome-modeling-simulation

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Resources for learning about modeling and simulation

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README 

        
# Awesome Modeling & Simulation Awesome Badge [![LinkCheck Action Status](https://github.com/comp-physics/awesome-modeling-simulation/workflows/LinkChecker/badge.svg)](https://github.com/comp-physics/awesome-modeling-simulation/actions)



Resources for learning about modeling and simulation.

This document is a work in progress, but nevertheless contains useful information.

Background expected in linear algebra and a typical calculus sequence.



_Disclaimer:_ Most linked content is _not_ licensed, owned, or maintained by S. H. Bryngelson, nor can I ensure the correctness of any of the below resources. 

Use for educational purposes and at your own risk.



## Table of contents 



- [Linear algebra refresher](#linear-algebra-refresher)

- [How to build a mathematical model?](#how-to-build-a-mathematical-model)

- [Discrete versus continuous time models](#discrete-versus-continuous-time-models)

- [Analysis of dynamical systems](#analysis-of-dynamical-systems)

  - [1D dynamical systems](#1d-dynamical-systems)

  - [2D+ dynamical systems](#2d-dynamical-systems)

- [Numerical methods for ODEs and PDEs](#numerical-methods-for-odes-and-pdes)

- [Cellular automata](#cellular-automata)

- [Markov chain model](#markov-chain-model)

- [Discrete-event simulation and queuing models](#discrete-event-simulation-and-queuing-models)

- [Input-output analysis](#input-output-analysis)

- [Creating dynamical systems from observations](#creating-dynamical-systems-from-observations)



## Linear algebra refresher 



- [Gilbert Strang lectures on Linear Algebra ](https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D)



- [Introduction to Linear and Matrix Algebra (Nathaniel Johnston) (textbooks)](https://link.springer.com/book/10.1007/978-3-030-52811-9)



- [Linear Algebra Done Right (Axler, Sheldon Jay) (textbooks)](https://linear.axler.net/)



- [Numerical Linear Algebra (Lloyd N. Trefethen, David Bau III) (textbooks)](https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617)



## How to build a mathematical model?



- [Introduction to Mathematical Modelling (slides, Prof. Das)](https://www.slideshare.net/arupparia/introduction-to-mathematical-modelling-42588379)



- [Intro. to mathematical modeling (slides, Andrea Doescl-Wilson)](https://jvanderw.une.edu.au/Lecture1_IntroToMathModelling.pdf)



- [An Introduction to Mathematical Modelling (course lecture notes, Glenn Marion)](https://people.maths.bris.ac.uk/~madjl/course_text.pdf)



- [How to build a mathematical model? (notes from Kata Murty)](http://www-personal.umich.edu/~murty/510/510slides1.pdf)



- [Introduction to Modeling and Simulation (slides from Markus J. Buehler, MIT)](https://ocw.mit.edu/courses/3-021j-introduction-to-modeling-and-simulation-spring-2012/resources/mit3_021js12_p1_l1/)



## Discrete versus continuous time models



- [Linear System Representation- MATLAB & Simulink Documentation](https://www.mathworks.com/help/control/linear-system-modeling.html?s_tid=CRUX_lftnav)



- [Basic Models- including continuous and discrete time models](https://www.mathworks.com/help/control/fixed-coefficient-models.html)



## Analysis of dynamical systems



### 1D dynamical systems



- [One dimensional Systems (video)](https://www.youtube.com/watch?v=YNIm2Op7UPg)



- [Geometric Approach 1D systems](http://www.ccs.fau.edu/~fuchs/pub/Huys_nonlin.pdf)



- [Princeton Notes for 1D systems (Pillow Lab)](http://pillowlab.princeton.edu/teaching/mathtools21fall/notes/notes_Dynamics.pdf)



- [Cornell Notes for 1D systems (Jonathan Victor)](http://www-users.med.cornell.edu/~jdvicto/jdv/mathcourse1617/mathcourse1617_Drover.pdf)



### 2D+ dynamical systems



- [Two dimensional linear systems (video)](https://www.youtube.com/watch?v=QrHRaA93Nrg)



- [Two dimensional nonlinear systems fixed points (video)](https://www.youtube.com/watch?v=9yh9DmNqdk4)



- [Bifurcations in two dimensional systems (video)](https://www.youtube.com/watch?v=oqKAVqe71vw)



- [Cornell Notes for 2D systems (Jonathan Victor)](http://www-users.med.cornell.edu/~jdvicto/jdv/mathcourse1617/mathcourse1617_Boie.pdf)



- [Introduction to Complex Systems (Dirk Brockmann)](https://rocs.hu-berlin.de/courses/complex-systems-2021/script/2-d-systems/)



## Numerical methods for ODEs and PDEs



- [Numerical Analysis 9th Ed (textbooks)](https://www.amazon.com/Numerical-Analysis-9th-Book-Only/dp/B0059JHM6M)



- [Differential equations (3Blue1Brown video playlist)](https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6)



- [Introduction to Numerical Simulation (MIT OpenCourseware, slides)](https://ocw.mit.edu/courses/6-336j-introduction-to-numerical-simulation-sma-5211-fall-2003/pages/lecture-notes/)



## Cellular automata



- [2D cellular automata demo (github repo)](https://github.com/Chakazul/Lenia) 



- [Cellular Automata Simulator](https://www.fourmilab.ch/cellab/manual/chap1.html)



- [Towards DataScience Article](https://towardsdatascience.com/algorithmic-beauty-an-introduction-to-cellular-automata-f53179b3cf8f)



## Markov chain model



- [Markov chain application: Google’s PageRank algorithm (slides)](https://www2.math.upenn.edu/~kazdan/312F12/JJ/MarkovChains/markov_google.pdf)



- [Markov Chains & PageRank](https://disco.ethz.ch/courses/fs16/ti2/lecture/chapter11.pdf)



- [Markov Chain Model Git repos](https://github.com/topics/markov-chain-model)



## Discrete-event simulation and queuing models



- Notes and Papers



  - [Discrete-event simulation of queuing systems](https://phyweb.physics.nus.edu.sg/~phytaysc/articles/queue.pdf)

  

  - [Discrete-Event Simulation](https://www.cs.bu.edu/faculty/matta/Teaching/cs655-papers/shankar-des.pdf)



- Explanatory videos by MATLAB Tech Talks



  - [What Is Discrete Event Simulation](https://www.youtube.com/watch?v=21WQB0E-6-M)



  - [Why Use Discrete Event Simulation](https://www.youtube.com/watch?v=adkeGlcqBAo)



  - [Leveraging Stochastic Processes](https://www.youtube.com/watch?v=3EiniZbyeV0)



  - [In context of Operations Research](https://www.youtube.com/watch?v=YkUT3fFrjpg)

  

  - [Example of DES in digital communication systems (video)](https://www.youtube.com/watch?v=w6SSng58DEw)



- Implementation/Code Examples



  - [Event discrete simulation with SimPy (video)](https://www.youtube.com/watch?v=Bk91DoAEcjY)



  - [Simulating a Queue (video)](https://www.youtube.com/watch?v=WEA8m3j-Jqk)

  

  - [Examples of using Python to write discrete-event simulations (video)](https://www.youtube.com/watch?v=0KvA92ykPKI))



  - [Python code example](https://github.com/mwong009/simulation)



## Input-output analysis



- [Textbook about control systems (book, via GitHub repo)](https://github.com/lugh56/control-and-system-book)



- [Input Modeling](https://softwaresim.com/blog/input-modeling-as-a-foundation-for-simulation/)



## Creating dynamical systems from observations



  - [An Experimentalist’s Introduction to the Observation of Dynamical Systems](https://www.worldscientific.com/doi/10.1142/9789814415729_0012)

  

  - [Introduction to Learning Dynamical Systems](https://cs.brown.edu/research/ai/dynamics/tutorial/Documents/DynamicalSystems.html)



  - [Learning Dynamical Systems from Partial Observations](https://arxiv.org/pdf/1902.11136.pdf)



  - [Learning Dynamical Systems from Data](https://www.sciencedirect.com/science/article/pii/S0167278922002500)