Gianluigi Rozza - Böcker

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications.This book will be of interest to researchers and graduate students in the field of reduced order modeling.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017.

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.

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.

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.

The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling.In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.

The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling.In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.

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 students.

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 students.

This book presents up-to-date state of the art for industrial mathematics and covers emerging topics in computational sciences. Mathematical models and computational methods have gained an increasing importance in the simulation of real-world and industrial problems. The employment of such methodologies deeply changed the standard ways of conceiving daily industrial production and strategies for sustainable exploitation of modern cities. The goal pursued by this book is twofold. On the one hand, cases of successful interaction between mathematics and industry are presented. Special emphasis is devoted to the benefits provided by the transfer of knowledge in different fields of applications, including the social challenges of sustainable development. On the other hand, groundbreaking ideas and emerging technologies in computational science are discussed to foster cross-fertilization of academic solutions and real-world problems. Math to Product (M2P) is meant to establish a platform for proposal, discussion, and promotion of current and new trends in industry, sustainability, and innovation, with the goal of supporting creative and interdisciplinary thoughts. Scientific/technical areas covered include transfer of knowledge, innovation in design, computational science and engineering, industrial optimization processes, sustainable mobility, aerospace, automotive, nautical and naval engineering.  Target audience is made up by grad students and researchers in the field.

This volume gathers peer-reviewed papers from the workshop Scientific Machine Learning: Emerging Topics, held at SISSA in Trieste, Italy. The event gathered leading researchers in mathematics, algorithms, and machine learning. Its goal was to advance the synergy between data-driven models and scientific computing, promoting robust, interpretable, and scalable methods. The works reflect major trends in scientific machine learning (SciML), including optimization, physics-informed learning, neural graph/operators/ODE, transformers, and generative models. Contributions propose physics-based constrained neural networks, advancements in optimization and model reduction, and applications across power systems, chemical kinetics, and biomechanics. Topics span from hybrid models for image classification to generative compression and neural operators for high-dimensional systems. Blending theory and practice, the volume captures the diversity and innovation shaping modern SciML.This volume is addressed to researchers and will provide readers with insight into the current state of the field, sparks new ideas, and encourages further research at the rich intersection of machine learning, mathematics, and scientific computing.

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effort, carried out over the last 12 years, to build a growing research community in this field.Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effort, carried out over the last 12 years, to build a growing research community in this field.Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.

This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system.