Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry

Abstract

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a onedimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schrödinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase.
Fichier principal
Vignette du fichier
main.pdf (4.07 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04131764 , version 1 (16-06-2023)
hal-04131764 , version 2 (28-07-2023)

Identifiers

  • HAL Id : hal-04131764 , version 2

Cite

Maxime Dalery, Geneviève Dusson, Virginie Ehrlacher, Alexei Lozinski. Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry. 2023. ⟨hal-04131764v2⟩
89 View
54 Download

Share

Gmail Mastodon Facebook X LinkedIn More