Premium
Data‐Driven Learning of Reduced‐Order Dynamics for a Parametrized Shallow Water Equation
Author(s) -
Yıldız Süleyman,
Goyal Pawan,
Benner Peter,
Karasözen Bülent
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000360
Subject(s) - subspace topology , projection (relational algebra) , dependency (uml) , partial differential equation , galerkin method , reduction (mathematics) , shallow water equations , model order reduction , predictability , mathematics , parametric statistics , computer science , mathematical optimization , construct (python library) , algorithm , artificial intelligence , mathematical analysis , finite element method , statistics , engineering , geometry , structural engineering , programming language
A non‐intrusive data‐driven model order reduction method is introduced that learns low‐dimensional dynamical models for a parametrized non‐traditional shallow water equation (NTSWE) [1]. The reduced‐order model is learnt by setting an appropriate least‐squares optimization problem [2] in a low‐dimensional subspace. The non‐intrusive model order reduction framework is extended to a parametric case using the parameter dependency at the level of the partial differential equation. The efficiency of the proposed non‐intrusive method is illustrated to construct reduced‐order models for NTSWE and compared with an intrusive method, proper orthogonal decomposition with Galerkin projection. Furthermore the predictability of both models outside the range of the training data is discussed.