MI (1381) - INGEGNERIA ELETTRICA / ELECTRICAL ENGINEERING

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057761 - MODELLING FROM MEASUREMENTS

Programma dettagliato e risultati di apprendimento attesi

Data-driven dynamical systems is a new interesting field connected to modelling nonlinear systems starting from measurements coming from the field. The course will describe the most recent advances on numerical techniques able to make use of a set of measurements from the fiels to extract a dynamic model of a physical process. The models then can be used both to predict the behaviour of the system in the near future and to provide indications to control it for the best. This is a critically important new direction, because the governing equations of many problems under consideration by practitioners in various scientific fields are typically not known. Hence, using data to help derive, in an optimal sense, the best dynamical system representation of a given process allows for important new insights for both the analysis and the control of the system. At the end of the course, the students will be able to use the proposed techniques in their own engineering field to synthetise dynamic models of the studied phenomena, starting from a reasonably large set of measurements coming from the field.

Note Sulla Modalità di valutazione

Project to be carried out at the end of the course.

Intervallo di svolgimento dell'attività didattica

Data inizio

Data termine

Calendario testuale dell'attività didattica

The course will deal with the following main topics: Singular Value Decomposition (SVD) & Principal Components (PCA) Overview of Supervised & Unsupervised Learning Dynamic Mode Decomposition (DMD) & Koopman Theory SINDy: Sparse ldentication of Nonlinear Dynamics Partial differential equation discovery Data Assimilation Methods & Kalman Filters Neural Networks Overview Gradient Descent & Backpropagation Neural Networks for Dynamics Autoencoders and Dynamics Optimal Sensor Placement Sparse Measurements and Cost Constraints

Bibliografia

J.Nathan Kutz, Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data, Editore: Oxford University Press, ISBN: 978-0199660346

Software utilizzato

Nessun software richiesto

Mix Forme Didattiche

Tipo Forma Didattica

Ore didattiche

lezione

20.0

esercitazione

12.0

laboratorio informatico

0.0

laboratorio sperimentale

0.0

progetto

0.0

laboratorio di progetto

0.0

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Note Docente

The course will be taught (25 hours) by prof. Prof. Nathan J. Kutz, University of Washington Professor Kutz was awarded the B.S. in Physics and Mathematics from the University of Washington in 1990 and the PhD in Applied Mathematics from Northwestern University in 1994. Following postdoctoral fellowships at the Institute for Mathematics and its Applications (University of Minnesota, 1994-1995) and Princeton University (1995-1997), he joined the faculty of applied mathematics and served as Chair from 2007-2015. His main research interests are related to numerical methods and scientific computing, data analysis and dimensionality reduction (PCA, POD, etc) methods, dynamical systems, bifurcation theory, linear and nonlinear wave propagation, perturbation and asymptotic methods, nonlinear analysis, variational methods, soliton theory, nonlinear optics, mode-locked lasers, fluid dynamics, Bose-Einstein condensation, neuroscience, gesture recognition and video & image processing.