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
1Introduction 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
2Introduction 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
3Dynamical 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
4Cellular 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
4.2
19 ReviewsTop Reviews
By EM•Nov 18th 2017
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!
By AR•Apr 18th 2018
Excellent course for people who love math, physics and simulations ! I choose it to get an insight on Lattice Boltzmann Method, I was happy to apply it and extend it to other cases.
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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