2019/06/12 by Carmen Gräßle, Gräßle, Carmen, Michael Hinze +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #A priori and a posteriori #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Basis (linear algebra) #Computer science #FOS: Mathematics #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Model order reduction #Nonlinear system #Numerical Analysis (math.NA) #Numerical methods for differential equations #Parametric statistics #Point of delivery #Proper orthogonal decomposition #Reduction (mathematics) #Statistics
paper · open access · doi:10.48550/arxiv.1906.05188
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from the infinite-dimensional perspective, reduction of nonlinearities, certification with a priori and a posteriori error estimates, spatial and temporal adaptivity, input dependency of the POD surrogate model, POD basis update strategies in optimal control with surrogate models, and sketch related algorithmic frameworks. The perspective of the method is demonstrated with several numerical examples.