About this Course

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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.

Learner Career Outcomes

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Flexible deadlines

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Approx. 33 hours to complete

Suggested: 6 hours/week...

English

Subtitles: English

Learner Career Outcomes

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Approx. 33 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

Week

5

2 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

Computational Fluid Dynamics: Overview11m

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

6

2 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

Particles and point-like objects: Overview6m

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

7

1 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

Introduction to Discrete Events8m

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

8

2 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

Motivation7m

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

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