|SCIENTIFIC DISCIPLINARY SECTOR
The module provides the mathematical basis for the analysis af large databases and it is focused on the practical application to fluid machinery problems.
AIMS AND CONTENT
The module aims to provide the mathematical tools for the analysis of large databases of experiments and numerical simulations. The students will learn to identify the principal components of the systems, and to develop the reduced order model that better represents the database from a statistics and dynamical point of view. The tools developed during the course are applied to the study of fluid machinery, but may be applied to different engineering problems.
AIMS AND LEARNING OUTCOMES
The student should be able to:
- Develop post-processing routines by means of Matlab for the elaboration of Big-Data in the field of fluid machinery. Particularly, the student should be able to develop programs for the identification of the principal information of a data-set and for the extraction of the best regression model
- Interpret the results of the modal decomposition techniques (e.g., Proper Orthogonal Decomposition and Dynamic Mode Decomposition) that will be introduced during the course
- Identify the best method for the reduction of a set of data, according to the data topology and the engineering parameters at hand.
- Understand and demonstrate the theory behind some of the recent Machine Learning techniques.
Frontal lessons will be mainly employed in the course. The lectures consist of a theoretical part followed by a practical implementation by means of Matlab routines. It is strongly suggested the participation of the student to the lessons, since the examination is driven by arguments discussed and presented during the lessons
The module aims to provide the basic theory of big-data analysis. The module is focused on techniques for dimensionality reduction and recent Machine Learning methods. The main chapters of the module are:
1. Dimensionality reduction: Fourier transform and Singular Value Decomposition (SVD).
2. Machine learning and data analysis: regression and model selection, classification, and neural networks.
3. Reduced Order Models: applications of the Proper Orthogonal Decomposition (POD).
4. Data-Driven analysis of a dynamical system: application of the Dynamic Mode Decomposition (DMD).
5. Each argument is followed by the practical application by means of programs written in the Matlab language. The student will be able to develop its own code for the analysis of big-data, with specific applications to fluid-machinery.
Brunton, Steven L., and J. Nathan Kutz. Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2019.
Dreyfus, Gérard. Neural networks: methodology and applications. Springer Science & Business Media, 2005.
TEACHERS AND EXAM BOARD
DAVIDE LENGANI (President)
L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.
The examination is composed of two parts. The first consists in the discussion of an exercise focused on the post-processing of different databases available to the research group of the professor, and provided to the student during the course. In the second part, an oral discussion of theoretical topics treated in the lessons will conclude the examination.
Students with SLD, disability or other regularly certified special educational needs are advised to contact the instructor at the beginning of the course to agree on teaching and examination methods that, in compliance with the course objectives, take into account the individual learning requirements.
The oral examination will allow verifying the acquired knowledge of the student regarding the theory of the different data reduction techniques, as well as their mathematical foundations. The discussion of a Matlab program aimed at the statistical and dynamical analysis of a big database will verify the capability of the student in the practical application.
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