|Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering
|COMPLEXITY REDUCTION IN SCIENTIFIC COMPUTING
|Credits (CFU / ECTS)
|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.
|Scientific-Disciplinary Sector (SSD)
Teaching Assignment Details