Contribution to a conference proceedings/Journal Article

PUBDB-2022-05027

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*

2023
Wiley-VCH Weinheim

This record in other databases:    

Please use a persistent id in citations: doi:10.1002/pamm.202200239  doi:10.3204/PUBDB-2022-05027

Abstract: Approximating functions in the linear span of truncated basis sets is a fundamental process in mathematical modelling with applications mainly to solving differential and integral equations. Such approximation schemes typically have nice properties such as the existence of convergence guarantees and the analysis of their order of convergence. However, these schemes generally suffer from the curse of dimensionality and their approximation capabilities are limited when the objective functions are highly oscillatory. Nonlinear approximators, e.g., neural networks, were proven to be very efficient in approximating high-dimensional functions. However, the lack of convergence guarantees for these models makes them less reliable in solving differential equations. Here, we investigate nonlinear approximators that are constructed by composing standard basis sets with normalizing flows. We showed that such models define a richer approximation space and conserve the density properties of the initial basis set. Simulations to approximate eigenfunctions of a perturbed quantum harmonic oscillator indicate convergence with 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 2023

---

Database coverage:
; ; ; DEAL Wiley ; Ebsco Academic Search

---

---

Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint 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
[10.48550/ARXIV.2212.01383]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

---