In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring
a prominence never imagined. In the past, in the domain of materials, processes and …

This book results from a course developed by the author and reflects both his own and
collaborative research regarding the development and implementation of uncertainty …

This paper revisits a new model reduction methodology based on the use of separated
representations, the so called Proper Generalized Decomposition—PGD. Space and time …

We put forward a general machine learning-based topology optimization framework, which
greatly accelerates the design process of large-scale problems, without sacrifice in …

Alfio Quarteroni Third Edition Page 1 MS&A – Modeling, Simulation and Applications 16
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …

In this paper we are addressing a new paradigm in the field of simulation-based engineering
sciences (SBES) to face the challenges posed by current ICT technologies. Despite the …

Over the past years, model reduction techniques have become a necessary path for the
reduction of computational requirements in the numerical simulation of complex models. A …

We review the foundations and applications of the proper generalized decomposition (PGD),
a powerful model reduction technique that computes a priori by means of successive …