Awesome Modeling & Simulation

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
• How to build a mathematical model?
• Discrete versus continuous time models
• Analysis of dynamical systems
  • 1D dynamical systems
  • 2D+ dynamical systems
• Numerical methods for ODEs and PDEs
• Cellular automata
• Markov chain model
• Discrete-event simulation and queuing models
• Input-output analysis
• Creating dynamical systems from observations

Linear algebra refresher

• Gilbert Strang lectures on Linear Algebra

• Introduction to Linear and Matrix Algebra (Nathaniel Johnston) (textbooks)

• Linear Algebra Done Right (Axler, Sheldon Jay) (textbooks)

• Numerical Linear Algebra (Lloyd N. Trefethen, David Bau III) (textbooks)

How to build a mathematical model?

• Introduction to Mathematical Modelling (slides, Prof. Das)

• Intro. to mathematical modeling (slides, Andrea Doescl-Wilson)

• An Introduction to Mathematical Modelling (course lecture notes, Glenn Marion)

• How to build a mathematical model? (notes from Kata Murty)

• Introduction to Modeling and Simulation (slides from Markus J. Buehler, MIT)

Discrete versus continuous time models

• Linear System Representation- MATLAB & Simulink Documentation

• Basic Models- including continuous and discrete time models

Analysis of dynamical systems

1D dynamical systems

• One dimensional Systems (video)

• Geometric Approach 1D systems

• Princeton Notes for 1D systems (Pillow Lab)

• Cornell Notes for 1D systems (Jonathan Victor)

2D+ dynamical systems

• Two dimensional linear systems (video)

• Two dimensional nonlinear systems fixed points (video)

• Bifurcations in two dimensional systems (video)

• Cornell Notes for 2D systems (Jonathan Victor)

• Introduction to Complex Systems (Dirk Brockmann)

Numerical methods for ODEs and PDEs

• Numerical Analysis 9th Ed (textbooks)

• Differential equations (3Blue1Brown video playlist)

• Introduction to Numerical Simulation (MIT OpenCourseware, slides)

Cellular automata

• 2D cellular automata demo (github repo)

• Cellular Automata Simulator

• Towards DataScience Article

Markov chain model

• Markov chain application: Google’s PageRank algorithm (slides)

• Markov Chains & PageRank

• Markov Chain Model Git repos

Discrete-event simulation and queuing models

• Notes and Papers

  • Discrete-event simulation of queuing systems

  • Discrete-Event Simulation

• Explanatory videos by MATLAB Tech Talks

  • What Is Discrete Event Simulation

  • Why Use Discrete Event Simulation

  • Leveraging Stochastic Processes

  • In context of Operations Research

  • Example of DES in digital communication systems (video)

• Implementation/Code Examples

  • Event discrete simulation with SimPy (video)

  • Simulating a Queue (video)

  • Examples of using Python to write discrete-event simulations (video))

  • Python code example

Input-output analysis

• Textbook about control systems (book, via GitHub repo)

• Input Modeling

Creating dynamical systems from observations

• An Experimentalist’s Introduction to the Observation of Dynamical Systems

• Introduction to Learning Dynamical Systems

• Learning Dynamical Systems from Partial Observations

• Learning Dynamical Systems from Data