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.
Simulation and modeling of natural processes
Offered By
University of Geneva
Syllabus - What you will learn from this course
Week
12 hours to complete
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 (Total 85 min), 1 reading, 1 quiz
7 videos
Modeling and Simulation13m
Modeling Space and Time15m
Example of bio-medical Modeling9m
Monte Carlo methods I9m
Monte Carlo methods II15m
Monte Carlo methods III10m
1 reading
Course slides10m
1 practice exercise
Introduction and general concepts8m
Week
22 hours to complete
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 (Total 94 min), 2 readings, 3 quizzes
12 videos
Concepts of code optimization6m
Concepts of parallelism4m
Palabos, a parallel lattice Boltzmann solver5m
An introduction to Python 36m
Running a Python program6m
Variables and data types11m
Operators8m
Conditional Statements7m
Loops7m
Functions15m
NumPy11m
2 readings
Course slides10m
Dive into python 310m
3 practice exercises
Introduction to programming with Python 310m
Project - Piles2m
Project - Class:Integration2m
Week
33 hours to complete
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 (Total 92 min), 3 readings, 3 quizzes
9 videos
The random walk14m
Growth of a population8m
Balance equations I8m
Balance equations II13m
Integration of ordinary differential equations7m
Error of the approximation8m
The implicit Euler scheme11m
Numerical integration of partial differential equations13m
3 readings
Course slides10m
References for numerical analysis10m
A reference for the random walk10m
3 practice exercises
Dynamical systems and numerical integration8m
The implicit Euler scheme18m
Project - Lotka-Volterra8m
Week
42 hours to complete
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 (Total 108 min), 2 readings, 2 quizzes
7 videos
Historical background9m
A mathematical abstraction of reality20m
Cellular Automata Models for Traffic13m
Complex systems20m
Lattice-gas models9m
Microdynamics of LGA17m
2 readings
Course slides10m
Notes on the Parity Rule10m
2 practice exercises
Cellular Automata8m
Project - The Parity Rule6m
Week
52 hours to complete
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 (Total 94 min), 1 reading, 4 quizzes
8 videos
Equations and challenges9m
From Lattice Gas to Lattice Boltzmann9m
Macroscopic Variables13m
Collision step: the BGK model12m
Streaming Step8m
Boundary Conditions21m
Flow around an obstacle6m
1 reading
Course slides10m
4 practice exercises
Optional - Equations and challenges2m
Lattice Boltzmann modeling of fluid flow4m
Project - Flow around a cylinder2m
Collision Invariant6m
Week
62 hours to complete
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 (Total 86 min), 1 reading, 2 quizzes
6 videos
Newton’s laws of motion, potentials and forces15m
Time-integration of equations of motion10m
The Lennard-Jones potential: Introducing a cut-off distance16m
The n-body problem: Evaluation of gravitational forces21m
Barnes-Hut algorithm: using the quadtree16m
1 reading
Course slides10m
2 practice exercises
Particles and point-like objects6m
Project - Barnes-Hut Galaxy Simulator2m
Week
71 hour to complete
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 (Total 70 min), 1 reading, 2 quizzes
6 videos
Definition of Discrete Events Simulations8m
Optimisation problems11m
Implementation matters9m
Traffic intersection12m
Volcano ballistics19m
1 reading
Course slides10m
2 practice exercises
Introduction to Discrete Event Simulation6m
Project - Simple modelling of traffic lights2m
Week
82 hours to complete
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 (Total 71 min), 1 reading, 2 quizzes
6 videos
Agents9m
Multi-Agent systems9m
Implementation of Agent Based Models15m
Ants Corpse clustering16m
Bacteria chemotaxy12m
1 reading
Course slides10m
2 practice exercises
Agent based models6m
Project - Multi-agents model6m
4.2
26 ReviewsTop Reviews
This course was a perfect match with my expectations! I think it is a perfect introduction to Computer modeling of natural processes. I enjoyed lectures and tasks. Thank you very much!
Instructors
Bastien Chopard
Full ProfessorComputer Science
Jean-Luc Falcone
Research AssociateComputer Science
Jonas Latt
Senior LecturerComputer Science
Orestis Malaspinas
Research AssociateComputer Science Department
About University of Geneva
Founded in 1559, the University of Geneva (UNIGE) is one of Europe's leading universities. Devoted to research, education and dialogue, the UNIGE shares the international calling of its host city, Geneva, a centre of international and multicultural activities with a venerable cosmopolitan tradition.
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