Augmenting Basis Sets by Normalizing Flows

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.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Augmenting Basis Sets by Normalizing Flows ; volume:23 ; number:1 ; year:2023 ; extent:6 ; Proceedings in applied mathematics and mechanics ; 23, Heft 1 (2023) (gesamt 6)

Contributors, Places and Time

• Creator: Saleh, Yahya ; Iske, Armin ; Yachmenev, Andrey ; Küpper, Jochen

Further information

• DOI: 10.1002/pamm.202200239
• URN: urn:nbn:de:101:1-2023060115131873382754
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:51 AM CEST