Numerical simulation laboratory

A.Y. 2020/2021
6
Max ECTS
60
Overall hours
SSD
FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08
Language
Italian
Learning objectives
Simulation is an essential tool in studying complex systems, anticipating, complementing and reinforcing both experimental and theoretical approaches. The purpose of this computing laboratory is to introduce and apply advanced Monte Carlo sampling and other techniques to perform simulations of complex systems and to solve complex numerical tasks.
The course aims to provide students with:
1) advanced techniques for sampling random variables and simulate stochastic processes
2) familiarity with the applications of these techniques to the simulation of complex systems
3) an introduction to some computational intelligence techniques
4) an introduction to parallel computation and parallel programming
Expected learning outcomes
The course aims to provide students with:
· advanced techniques for sampling random variables and simulate stochastic processes
· familiarity with the applications of these techniques to the simulation of complex systems
· an introduction to some computational intelligence techniques, machine learning and deep neural networks
· an introduction to parallel computation and parallel programming
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Teaching can be provided remotely if there are mobility limitations related to the Covid-19 health emergency. In this case, asynchronous lessons will be made available (powerpoint auditions), organized to cover the topics of each lesson of the teaching. The exercises will take place with synchronous remote videoconferencing connections with the Zoom platform. The auditions will be made available to students on the ARIEL teaching platform for the entire semester. In addition, weekly synchronous meetings with students will be organized, always using the Zoom platform, in order to provide clarifications and insights on teaching topics and answer students' questions.
Course syllabus
· Probability theory, stochastic processes, mathematical statistics
· Sampling of random variables and Monte Carlo integration
· Markov chains, Metropolis algorithm
· Numerical simulations in classical and quantum statistical mechanics
· Stochastic calculus and stochastic differential equation with applications
· Computational intelligence, stochastic optimization, statistical analysis of inverse problems
· Introduction to parallel computing and parallel programming
· Introduction to machine learning and deep neural networks
Prerequisites for admission
Knowledge of C ++ programming language
Teaching methods
Delivery method: traditional, lectures and numerical exercises
Attendance: mandatory
Teaching Resources
· E. Vitali, M. Motta, D.E. Galli "Theory and Simulation of Random Phenomena" Springer Unitext (in press)
· M.E.J. Newman and G.T. Barkema "Monte Carlo Methods in Statistical Physics", Clarendon Press
· D. Frenkel and B. Schmidt "Understanding Molecular Simulation", Academic Press
· W. Krauth "Statistical Mechanics -Algorithms and Computations" Oxford University Press
· P. Glasserman "Monte Carlo Methods in Financial Engineering" Springer
· The material presented and discussed in the individual lectures and laboratory exercises is made available on the Ariel website of the course: https://dgallilsn.ariel.ctu.unimi.it
Assessment methods and Criteria
The examination consists in the delivery of a series of numerical exercises and an oral discussion regarding the numerical exercises delivered in the light of the topics dealt with in the laboratory. The correctness of the numerical exercises, the quality of the data analysis carried out on the results of the simulations and the programming style are evaluated. At the end of the teaching the student will have to know advanced methods to sample random variables and know how to use them to set up simulations of complex systems.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 0
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0
FIS/03 - PHYSICS OF MATTER - University credits: 0
FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0
FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM - University credits: 0
FIS/07 - APPLIED PHYSICS - University credits: 0
FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS - University credits: 0
Laboratories: 36 hours
Lessons: 24 hours