L'insegnamento prevede 3.0 CFU erogati con Didattica Innovativa come segue:
Blended Learning & Flipped Classroom
Corso di Studi
Codice Piano di Studio preventivamente approvato
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
055701 - COMPUTATIONAL STATISTICS
055700 - COMPUTATIONAL STATISTICS
This is a course about exploring random systems using computer simulations. Indeed, almost every mathematical model describing systems or phenomena of interest is hampered by uncertainties, although very often uncertain features or inputs are not accounted for.
The goal of the course is to introduce computational tools aiming at: (i) describing uncertainty sources in general systems, with special emphasis on differential models, and (ii) analyzing the impact of uncertainty on systems’ outcomes, in terms of both uncertainty propagation from inputs to outputs, and input parameter estimation from noisy observations.
Risultati di apprendimento attesi
Besides the knowledge of theoretical results and numerical methods presented during lectures and Lab sessions, a critical comprehension of the class’ topics is expected by the students at the end of the class, justifying the followed procedures. Attending the course, students are expected to:
know and understand how to perform numerical simulation of random processes and sampling methods, and how to tackle uncertainty quantification issues related with steady and unsteady systems;
adapt the proposed methodologies to problems of applied interest in Engineering;
interpret the results, assessing both accuracy and efficiency of simulation strategies, from both a numerical and a statistical point of view.
The course is organized in theoretical lectures and lab sessions. An additional project must be carried out in the form 5+3 CFU. Lectures will provide the theoretical background; practical Lab sessions will provide algorithms' implementation and examples of application of the considered methodologies by using basic Matlab codes.
Part 1. Numerical simulation of random processes and sampling methods
Random number generation: inversion method, transformations, rejection sampling.
Gaussian processes. Karhunen-Loève expansion.
Monte Carlo methods, estimates, error. Multi-level (or multi-fidelity) Monte Carlo methods.
Variance reduction techniques.
Part 2. Sensitivity analysis and forward Uncertainty Quantification
Surrogate models or emulators: polynomial chaos expansions, reduced-order models.
Uncertainty propagation through Monte Carlo methods. Application to differential models.
Part 3. Data assimilation and inverse Uncertainty Quantification
Statistical inverse problems: a Bayesian setting for parameter estimation.
Monte Carlo Markov Chain methods. Application to differential models.
Data assimilation: Kalman filters and particle filters. Application to differential models.
The course targets students following either a Computational Science and Engineering or an Applied Statistics track. Students are required to have a solid background in Statistics, Probability, Numerical Analysis. A solid background in Matlab programming is assumed.
Modalità di valutazione
In the 5CFU form, the exam consists of an oral test, covering the content of both theoretical lectures and practical Lab sessions.
In the 5+3CFU form, the grade of the oral test is 5/8 of the final grade, and an additional project dealing with some of the class topics, chosen among a list of proposed titles, has to be carried out, in teams of 1 to 3 students.
The project will consist of the use, adaptation or extension of some of the methods presented during the course, to a case of interest, starting, e.g., from the critical analysis of a recent scientific paper. Projects will be presented at the end of the course in short seminars during an open workshop that will take place after the end of the semester. The presentation of the project provides 3/8 of the final grade.
The course will be based on a selection of chapters of the following books, class notes, and some selected scientific papers provided:
Jochen Voss, An Introduction to Statistical Computing. A Simulation-based Approach., Editore: . John Wiley & Sons, Anno edizione: 2014
Ralph C Smith, Uncertainty Quantification: Theory, Implementation, and Applications, Editore: SIAM, Anno edizione: 2013
Jari Kaipio, Erkki Somersalo, Statistical and Computational Inverse Problems, Editore: Springer, Anno edizione: 2005
Mark Asch, Marc Bocquet, Maelle Nodet, Data Assimilation. Methods, Algorithms, and Applications, Editore: SIAM, Anno edizione: 2016
Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese