This book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields. Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity the dimension, the degrees of freedom, the data arising in these models. The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.

Written by internationally recognised experts in model order reduction and related areas Presents a fresh, very original and balanced selection of modern topics Features self-contained contributions, ideal for newcomers to the field

Inhalt

• 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.