Empirical sparse regression on quadratic manifolds-

作     者：Schwerdtner, Paul Gugercin, Serkan Peherstorfer, Benjamin 

作者机构：Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Nonlinear simulations 

摘      要：Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation spaces, limiting their effectiveness for data representing transport-dominated and wave-like dynamics. To address this limitation, we introduce quadratic manifold sparse regression, which trains quadratic manifolds with a sparse greedy method and computes approximations on the manifold through novel nonlinear projections of sparse samples. The nonlinear approximations obtained with quadratic manifold sparse regression achieve orders of magnitude higher accuracies than linear methods on data describing transport-dominated dynamics in numerical *** Codes 65F55, 62H25, 65F30, 68T09, 65F20, 65M22 Copyright © 2024, The Authors. All rights reserved.