Model Reduction of Parametrized Systems

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 effor

t, 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).

1 Two ways to treat time in Reduced Basis Methods.- 2 Simultaneous empirical interpolation and reduced basis method. Application to non-linear multi-physics problem.- 3 A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two-sided Control Constraints.- 4 A reduced basis method with an exact solution certificate and spatio-parameter adaptivity: application to linear elasticity.- 5 A Reduced Basis Method for Parameter Functions using Wavelet Approximations.- 6 Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics.- 7 Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media.- 8 Offline Error Bounds for the Reduced Basis Method.- 9 ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics.- 10 Reduced-order semi-implicit schemes for  fluid-structure interaction problems.- 11 True Error Control for the Localized Reduced Basis Method for Parabolic Problems.- 12 Automatic reduction of

PDEs defined on domains with variable shape.- 13 Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry.- 14 A-posteriori error estimation of discrete POD models for PDE-constrained optimal control.- 15 Hi-POD solution of parametrized fluid dynamics problems: preliminary results.- 16 Adaptive sampling for nonlinear dimensionality reduction based on manifold learning.- 17 Cross-Gramian-Based Model Reduction: A Comparison.- 18 Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction.- 19 Leveraging Sparsity and Compressive Sensing for Reduced Order Modeling.- 20 A HJB-POD approach to the control of the level set equation.- 21 Model order reduction approaches for infinite horizon optimal control problems via the HJB equation.- 22 Interpolatory methods for H model reduction of multi-input/multi-output systems.- 23 Model reduction of linear time-varying systems with applications for moving loads.- 24 Interpolation Strategy for BT-based Parametric MOR of Gas Pipeline-Networks.- 25 Energy stable model order reduction for the  Allen-Cahn equation.- 26 MOR-based Uncertainty Quantification in Transcranial Magnetic Stimulation.- 27 Model Order Reduction of Nonlinear Eddy Current Problems using Missing Point Estimation.- 28 On Efficient Approaches for Solving a Cake Filtration Model under Parameter Variation.- 29 Model reduction for coupled near-well and reservoir models using multiple space-time discretizations.- 30 Time-dependent Parametric Model Order Reduction for Material Removal Simulations