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Bibliographic resources
Bibliography mandatory
Bibliography not mandatory
Summary Teaching Assignment
Academic Year 2022/2023
Type of Teaching Doctorate
Course 058414 - COMPLEXITY REDUCTION IN SCIENTIFIC COMPUTING
Professor Manzoni Andrea
Cfu 5.00 Type of Course Mono-Disciplinary Course

Phd Programme From (included) To (excluded) Course
MI (1385) - MODELLI E METODI MATEMATICI PER L'INGEGNERIA / MATHEMATICAL MODELS AND METHODS IN ENGINEERINGAZZZZ058414 - COMPLEXITY REDUCTION IN SCIENTIFIC COMPUTING

Detailed program and learning outcomes

The goal of the course is to introduce and discuss the most recent trends of scientific computing aimed at reducing the complexity of numerical simulations, merging physics-based models with data in the spirit of uncertainty quantification, and leveraging the knowledge from different models. These techniques include reduced order modeling for parametrized systems, parameter estimation and data assimilation, Monte Carlo methods and their recent extensions to multi-fidelity techniques.

 

This course surveys the state-of-the-art of reduced order modeling strategies for the efficient numerical approximation of differential problems, their uncertainty quantification, and the possible use of a wealth of different models for the setting of multi-fidelity strategies. Starting from basic strategies like singular value decomposition, least squares methods and Monte Carlo integration, the course will explore recent trends in Scientific Computing aiming at (i) reducing the complexity of numerical simulations and (ii) exploiting numerical models to perform forward propagation of uncertainty and data assimilation, as well as (iii) leveraging knowledge from different models. Each of these three blocks will then be concluded by a survey of most recent trends like, e.g., nonlinear dimensionality reduction through deep learning, identification of nonlinear dynamics and model discovery, kernel methods. 

 

Due to the multi-faceted nature of the proposed topics, a bottom-up approach will be followed, considering few benchmark problems and simple case studies in order to discuss the main features of each methodology. Implementation of basic techniques will be possible thanks to Matlab/Python packages providing a user-friendly framework for their implementation.


Notes on methods of assessing

The evaluation will be based on a project related with the lectures’ topics, focusing on either applicative or methodological aspects. The project will include numerical simulations to be developed within the packages provided, or other code libraries.


Teaching activities
Start date
End date

Schedule planning

The course will focus on both the analysis of numerical methods and their application. Regular lectures and “Hands On” Sessions will be scheduled to present the most relevant techniques and to show their implementation. 

 

Classes will be held, tentatively, between January and February 2023. A detailed schedule will be provided in December 2022.

 

Students interested to the course can send an email to andrea1.manzoni@polimi.it. A mailing list will be used to share important information about classes (rooms, schedule modifications, ...)


Bibliography

Software used
No software required

Didactic forms
Type of didactic form Teaching hours
lesson
21.0
training
0.0
computer laboratory
0.0
experimental laboratory
5.0
project
0.0
project laboratory
0.0

Information in English to support internationalization
Course offered in language English
Study material/slides available in English
Textbook/Bibliography available in English
It is possible to take the examination in English
Support available in English

Note Professor
For more information please contact Andrea Manzoni (andrea1.manzoni@polimi.it).
schedaincarico v. 1.8.4 / 1.8.4
Area Servizi ICT
13/04/2024