Course Title

Modelling and Simulation for Scientific Applications

Course Code

SDS 423

Course Type

Elective

Level

Master’s

Year / Semester

2^nd Semester

Instructor’s Name

Prof. Vangelis Harmandaris

ECTS

5

Lectures / week

2

Laboratories / week

1

Course Purpose and Objectives

The aim of this course is to teach students to use simulation algorithms and to analyze their results in order to study complex systems.

This includes a focus on deterministic and stochastic simulation approaches for predicting the behavior of complex systems across a broad range of scientific areas from physical sciences, engineering and biology. Methods include, among others, Monte Carlo (MC) algorithms, multi-scale modeling approaches and molecular dynamics (MD) simulations. Moreover, the course focus on the coupling between simulations and data-driven algorithms.

The course will consist of exercises and a project worked out in groups. Each group will have to give a talk on the methodology and the results.

Learning Outcomes

By the end of the course, the students will have a good grasp on deterministic and stochastic simulations for investigating multi-scale phenomena associated with complex systems. They will be able to develop computational realistic models for studying realistic systems. At the same time they will have experience in state-of-the-art simulations methods such as Monte Carlo and Molecular Dynamics simulations. Moreover, the students will be able to use state-of-the-art supercomputers to perform demanding simulations of real life applications.

Prerequisites

Course Content

The content of the course on weekly basis include:

Week 1: Introduction to deterministic and stochastic systems; Basics of Statistical Physics. This includes a discussion on the Boltzmann distribution, fluctuations and correlation functions.

Week 2: Monte Carlo (MC) methods and MC Integration; Importance sampling;

Week 3: Markov Chain Monte Carlo (MCMC) and the Metropolis algorithms;

Week 4: Molecular dynamics (MD) algorithm for the simulations of molecular systems;

Week 5: Prediction of properties of complex systems by analyzing simulation outcome; Statistical errors and resampling techniques for MC/MD simulations; Autocorrelations in time series data from MCMC and/or MD simulations.

Weeks 6-7: Introduction in the concept of multi-scale modeling by providing a consistent coupling between microscopic (atomistic) and mesoscopic (coarse-grained) models for high dimensional molecular systems;

In addition a computational project will be given to the students, referring to the usage of MCMC and/or MD simulations for the study of high dimensional realistic model systems.

Teaching Methodology

Lectures, Labs, Project

Bibliography

• Understanding Molecular Simulation, From Algorithms to Applications, by Frenkel and B. Smit, Academic Press, San Diego, 2002
• Monte Carlo Strategies in Scientific Computing, by Liu, Springer, New York, 2001.
• Stochastic Methods: A Handbook for the Natural and Social Sciences, by Gardiner, Springer, New York, 2009.
• Building Software for Simulation (Wiley) by James Nutaro
• Computer Simulation in Physics and Engineering, by Steinhauser, Martin Oliver
• Numerical Recipes: The Art of Scientific Computing, by H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, 3rd Edition

Assessment

Combination of coursework and a project basis exam

Language

English