Preprint

PUBDB-2022-07441

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Augmenting Basis Sets by Normalizing Flows

Saleh, Y. (Corresponding author)CFEL*DESY* ; Iske, A.CFEL* ; Yachmenev, A.CFEL*DESY* ; Küpper, J.CFEL*XFEL.EU*DESY*

2022

This record in other databases:    

Please use a persistent id in citations: doi:10.48550/ARXIV.2212.01383

Report No.: arXiv:2212.01383

Abstract: Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by provable approximation orders. On the down side, however, these methods often suffer from the curse of dimensionality, which limits their approximation behavior, especially in situations of highly oscillatory target functions. Nonlinear approximation methods, such as neural networks, were shown to be very efficient in approximating high-dimensional functions. We investigate nonlinear approximation methods that are constructed by composing standard basis sets with normalizing flows. Such models yield richer approximation spaces while maintaining the density properties of the initial basis set, as we show. Simulations to approximate eigenfunctions of a perturbed quantum harmonic oscillator indicate convergence with respect to the size of the basis set.

Keyword(s): Numerical Analysis (math.NA) ; FOS: Mathematics ; G.1 ; 65K99

---

Contributing Institute(s):

1. CFEL-CMI (FS-CFEL-CMI)
2. beauftragt von UNI (UNI/CUI)
3. Uni Hamburg / Experimentalphysik (UNI/EXP)

Research Program(s):

1. 631 - Matter – Dynamics, Mechanisms and Control (POF4-631) (POF4-631)
2. HIDSS-0002 - DASHH: Data Science in Hamburg - Helmholtz Graduate School for the Structure of Matter (2019_IVF-HIDSS-0002) (2019_IVF-HIDSS-0002)
3. DFG project 390715994 - EXC 2056: CUI: Advanced Imaging of Matter (390715994) (390715994)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2022

---

---

Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Contribution to a conference proceedings/Journal Article Saleh, Y. (Corresponding author)CFEL*DESY* ; Iske, A.CFEL* ; Yachmenev, A.CFEL*DESY* ; Küpper, J.CFEL*XFEL.EU*DESY*
Augmenting basis sets by normalizing flows
202392nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, (GAMM), AachenAachen, Germany, 15 Aug 2022 - 19 Aug 20222022-08-152022-08-19 Proceedings in applied mathematics and mechanics 23(1), e202200239 (2023) [10.1002/pamm.202200239] special issue: "Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)"2023     Files  Fulltext BibTeX | EndNote: XML, Text | RIS

---