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.

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Flexible deadlines

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Approx. 31 hours to complete

Suggested: 6 hours/week...

English

Subtitles: English...

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Approx. 31 hours to complete

Suggested: 6 hours/week...

English

Subtitles: English...

Syllabus - What you will learn from this course

Week

1

2 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

Objectives and background11m

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

2

2 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

Introduction to high performance computing for modeling4m

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

3

3 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

General introduction to dynamical systems6m

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

4

2 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

Definition and basic concepts16m

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

Instructors

Frequently Asked Questions

When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
What is the refund policy?
Is financial aid available?

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Simulation and modeling of natural processes