This volume is focused on the review of recent algorithmic and mathematical advances and the development of new research directions for Mathematical Model Approximations via RAMSES (Reduced order models, Approximation theory, Machine learning, Surrogates, Emulators, Simulators) in the setting of parametrized partial differential equations also with sparse and noisy data in high-dimensional parameter spaces.The book is a valuable resource for researchers, as well as masters and Ph.D...

Joint replacement is a logical step in the treatment of severe joint pathologies with irreversible lesions resisting conservative therapy. At the spinal level, arthrodesis became, very early, the gold standard of treatment for severe intervertebral disc pathologies. The next logical step was to envision functional replacement, and this step was taken as early as 1956, when the first intervertebral implant was described. However, it took many more years and a great variety of proposed impla...

This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equat...