Titlebook: Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators; RAMSES Gianluigi Rozza,Giovanni Stabile,Marta D‘Elia Book

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1439-7358 e communities.Latest knowledge and results on emerging topic.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 learn

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1439-7358 ing, 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 students..978-3-031-55062-1978-3-031-55060-7Series ISSN 1439-7358 Series E-ISSN 2197-7100

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,Measuring Stiffness in Residual Neural Networks,asures numerically by examining their evolution over the course of training a ResNet on several test problems. We find that stiffness tends to increase as a result of training, and suggest the developed stiffness metrics can be used as training penalties, providing a novel means of regularization for ResNets.

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,Reduced Order Modelling of Nonaffine Problems on Parameterized NURBS Multipatch Geometries,differential equations. The introduction of IGA enables a unified simulation framework based on a single geometry representation for both design and analysis. The coupling of reduced basis methods with IGA has been motivated in particular by their combined capabilities for geometric design and solut