Numerical simulation laboratory

A.Y. 2019/2020
6
Max ECTS
62
Overall hours
SSD
FIS/02 FIS/03
Language
Italian
Learning objectives
Numerical simulation is an essential tool in studying complex systems, anticipating, complementing and reinforcing both experimental and theoretical approaches. The learning objectives of this computing laboratory are the introduction and application of advanced Monte Carlo sampling techniques to perform simulations of complex systems, of computational intelligence techniques to solve or optimize complex problems and, finally, of machine learning techniques and deep neural networks
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

Lesson period
Second semester
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 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, of about 40 minutes, 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
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0
FIS/03 - PHYSICS OF MATTER - University credits: 0
Laboratories: 48 hours
Lessons: 14 hours