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Dettaglio Insegnamento
| Academic Year |
2021/2022 |
| Name |
Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering |
| Programme Year |
1 |
| ID Code |
057418 |
| Course Title |
ADVANCED NUMERICAL METHODS FOR PREDICTIVE DIGITAL TWINS |
| Course Type |
MONODISCIPLINARE |
| Credits (CFU / ECTS) |
5.0 |
| Course Description |
This course surveys the state-of-the-art of uncertainty quantification and data assimilation for the discovery of dynamical systems, surrogate models and multi-fidelity techniques, including non-intrusive neural network approxima-tions of parametrized physical systems, data-driven tools for model identifica-tion that embed physical laws in the learning algorithm, resulting in physical-ly-consistent learnt models, physics-informed Machine Learning.
Due to the multi-faceted nature of the proposed topics, a bottom-up ap-proach will be followed, considering few benchmark problems and simple case studies in order to discuss the main features of each methodology, and to provide a comparative discussion that lend insights to potential ad-vantages/disadvantages entailed by their application.
Implementation of basic techniques will be possible thanks to Matlab/Python packages providing a user-friendly framework for their implementation.
Part I Introduction (5 hours)
Introduction to Digital Twins. The Digital twin paradigm in engineering (aerospace, manufacturing etc). The Digital Twin paradigm in life sciences (precision medicine, virtual clinical trials etc.)
A general paradigm for data-driven physics based digital twins.
Ideas from a study case of an Unmanned Air Vehicle.
Model order reduction, data assimilation and uncertainty quantification as main ingredients for the definition of the digital twin.
Part II Fundamental tools (9 hours)
Model order reduction
Uncertainty quantification
Data assimilation
Multifidelity models
Part III Machine learning inspired tools for digital twins (9 hours)
Physics informed neural networks (PINNs) for forward and inverse problems.
Hands on session on PINNs.
Model order reduction by deep learning approximation of differential operators (DL-ROMs).
Hands on session on DL-ROMs.
Part IV Applications (3 hours)
Applications of Digital Twins to precision medicine |
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Alphabetical group
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Professor
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Course details
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From (included)
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To (excluded)
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A
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ZZZZ
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Manzoni Andrea, Zunino Paolo
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