Simulation and modeling of natural processes

About this course: This course gives you an introduction to modeling methods and simulation tools for a wide range of natural phenomena. The different methodologies that will be presented here can be applied to very wide range of topics such as fluid motion, stellar dynamics, population evolution, ... This course does not intend to go deeply into any numerical method or process and does not provide any recipe for the resolution of a particular problem. It is rather a basic guideline towards different methodologies that can be applied to solve any kind of problem and help you pick the one best suited for you. The assignments of this course will be made as practical as possible in order to allow you to actually create from scratch short programs that will solve simple problems. Although programming will be used extensively in this course we do not require any advanced programming experience in order to complete it.

Created by:  University of Geneva

• Taught by:  Bastien Chopard, Full Professor

  Computer Science

• Taught by:  Jean-Luc Falcone, Research Associate

  Computer Science

• Taught by:  Jonas Latt, Senior Lecturer

  Computer Science

• Taught by:  Orestis Malaspinas, Research Associate

  Computer Science Department

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Syllabus


WEEK 1


Introduction and general concepts



This module gives an overview of the course and presents the general ideas about modeling and simulation. An emphasis is given on ways to represent space and time from a conceptual point of view. An insight of modeling of complex systems is given with the simulation of the grothw and thrombosis of giant aneurysms. Finally, a first class of modeling approaches is presented: the Monte-Carlo methods.


7 videos, 1 reading expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Objectives and background
3. Video: Modeling and Simulation
4. Video: Modeling Space and Time
5. Video: Example of bio-medical Modeling
6. Video: Monte Carlo methods I
7. Video: Monte Carlo methods II
8. Video: Monte Carlo methods III

Graded: Introduction and general concepts

WEEK 2


Introduction to programming with Python 3
This module intends to provide the most basic concepts of high performance computing used for modeling purposes. It also aims at teaching the basics of Python 3 which will be the programming language used for the quizzes in this course.


12 videos, 2 readings expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Introduction to high performance computing for modeling
3. Video: Concepts of code optimization
4. Video: Concepts of parallelism
5. Video: Palabos, a parallel lattice Boltzmann solver
6. Материал для самостоятельного изучения: Dive into python 3
7. Video: An introduction to Python 3
8. Video: Running a Python program
9. Video: Variables and data types
10. Video: Operators
11. Video: Conditional Statements
12. Video: Loops
13. Video: Functions
14. Video: NumPy

Graded: Introduction to programming with Python 3
Graded: Project - Piles
Graded: Project - Class:Integration

WEEK 3


Dynamical systems and numerical integration



Dynamical systems modeling is the principal method developed to study time-space dependent problems. It aims at translating a natural phenomenon into a mathematical set of equations. Once this basic step is performed the principal obstacle is the actual resolution of the obtained mathematical problem. Usually these equations do not possess an analytical solution and advanced numerical methods must be applied to solve them. In this module you will learn the basics of how to write mathematical equations representing natural phenomena and then how to numerically solve them.


9 videos, 1 reading expand

1. Материал для самостоятельного изучения: Course slides
2. Video: General introduction to dynamical systems
3. Video: The random walk
4. Video: Growth of a population
5. Video: Balance equations I
6. Video: Balance equations II
7. Video: Integration of ordinary differential equations
8. Video: Error of the approximation
9. Video: The implicit Euler scheme
10. Video: Numerical integration of partial differential equations

Graded: Dynamical systems and numerical integration
Graded: The implicit Euler scheme
Graded: Project - Lotka-Volterra

WEEK 4


Cellular Automata



This module defines the concept of cellular automata by outlining the basic building blocks of this method. Then an insight of how to apply this technique to natural phenomena is given. Finally the lattice gas automata, a subclass of models used for fluid flows, is presented.


7 videos, 2 readings expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Definition and basic concepts
3. Video: Historical background
4. Video: A mathematical abstraction of reality
5. Video: Cellular Automata Models for Traffic
6. Video: Complex systems
7. Video: Lattice-gas models
8. Video: Microdynamics of LGA
9. Материал для самостоятельного изучения: Notes on the Parity Rule

Graded: Cellular Automata
Graded: Project - The Parity Rule

WEEK 5


Lattice Boltzmann modeling of fluid flow



This module provides an introduction to the lattice Boltzmann method, a powerful tool in computational fluid dynamics. The lesson is practice oriented and show, step by step, how to write a program for the lattice Boltzmann method. The program is used to showcase an interesting problem in fluid dynamics, the simulation of a vortex street behind an obstacle.


8 videos, 1 reading, 1 practice quiz expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Computational Fluid Dynamics: Overview
3. Video: Equations and challenges
4. Video: From Lattice Gas to Lattice Boltzmann
5. Video: Macroscopic Variables
6. Video: Collision step: the BGK model
7. Video: Streaming Step
8. Video: Boundary Conditions
9. Video: Flow around an obstacle
10. Тренировочный тест: Optional - Equations and challenges

Graded: Lattice Boltzmann modeling of fluid flow
Graded: Project - Flow around a cylinder
Graded: Collision Invariant

WEEK 6


Particles and point-like objects



A short review of classical mechanics, and of numerical methods used to integrate the equations of motions for many interacting particles is presented. The student will learn that the computational expense of resolving all interaction between particles poses a major obstacle to simulating such a system. Specific algorithms are presented to allow to cut down on computational expense, both for short-range and large-range forces. The module focuses in detail on the Barnes-Hut algorithm, a tree algorithm which is popular a popular approach to solve the N-Body problem.


6 videos, 1 reading expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Particles and point-like objects: Overview
3. Video: Newton’s laws of motion, potentials and forces
4. Video: Time-integration of equations of motion
5. Video: The Lennard-Jones potential: Introducing a cut-off distance
6. Video: The n-body problem: Evaluation of gravitational forces
7. Video: Barnes-Hut algorithm: using the quadtree

Graded: Particles and point-like objects
Graded: Project - Barnes-Hut Galaxy Simulator

WEEK 7


Introduction to Discrete Events Simulation



In this module, we will see an alternative approach to model systems which display a trivial behaviour most of the time, but which may change significantly under a sequence of discrete events. Initially developed to simulate queue theory systems (such as consumer waiting queue), the Discrete Event approach has been apply to a large variety of problems, such as traffic intersection modeling or volcanic hazard predictions.


6 videos, 1 reading expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Introduction to Discrete Events
3. Video: Definition of Discrete Events Simulations
4. Video: Optimisation problems
5. Video: Implementation matters
6. Video: Traffic intersection
7. Video: Volcano ballistics

Graded: Introduction to Discrete Event Simulation
Graded: Project - Simple modelling of traffic lights

WEEK 8


Agent based models



Agent Based Models (ABM) are used to model a complex system by decomposing it in small entities (agents) and by focusing on the relations between agents and with the environment. This approach is derived from artificial intelligence research and is currently used to model various systems such as pedestrian behaviour, social insects, biological cells, etc.


6 videos, 1 reading expand

1. Материал для самостоятельного изучения: Course slides
2. Video: Motivation
3. Video: Agents
4. Video: Multi-Agent systems
5. Video: Implementation of Agent Based Models
6. Video: Ants Corpse clustering
7. Video: Bacteria chemotaxy

Graded: Agent based models
Graded: Project - Multi-agents model