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@INPROCEEDINGS{FernandezCorral:625360,
author = {Fernandez Corral, Alvaro},
title = {{T}he coordinate is right - {A}ugmenting basis sets via
normalizing flows},
reportid = {PUBDB-2025-01117},
year = {2025},
abstract = {Approximating functions using a basis set of the
functions’ space guarantees convergence of the
approximation. However, high-accuracy calculations require
memory costs that scale exponentially with the
dimensionality, formally known as the curse of
dimensionality. In this talk, I will introduce augmented
basis sets, generated by pushing forward standard basis sets
through normalizing flows, i.e., invertible neural networks,
which is equivalent to a transformation of the basis’
coordinates. Multidimensional basis sets are often built
from direct-products of univariate functions. These
constructions struggle to capture complex structures
involving different coordinates. Normalizing-flows
coordinates reduce the coupling between dimensions,
mitigating the curse of dimensionality.I will demonstrate
the efficacy of augmented basis sets to approximate
eigenpairs of the vibrational Schrödinger equation. Unlike
standard neural-network-based methods that directly model
the eigenfunctions, our method preserves the basis
properties, ensuring robustness in the approximation of many
highly excited states. Additionally, optimal
normalizing-flows coordinates encode physical information of
the molecular motion, which allows for the interpretability
of the method, and enables transferability to different
basis set truncations sizes and even to structurally similar
molecular systems.},
month = {Mar},
date = {2025-03-03},
organization = {Internal Conference on Scientific
Computing and Machine Learning, Kyoto
(Japan), 3 Mar 2025 - 7 Mar 2025},
subtyp = {Invited},
cin = {FS-CFEL-CMI},
cid = {I:(DE-H253)FS-CFEL-CMI-20220405},
pnm = {631 - Matter – Dynamics, Mechanisms and Control
(POF4-631) / HIDSS-0002 - DASHH: Data Science in Hamburg -
Helmholtz Graduate School for the Structure of Matter
$(2019_IVF-HIDSS-0002)$},
pid = {G:(DE-HGF)POF4-631 / $G:(DE-HGF)2019_IVF-HIDSS-0002$},
experiment = {EXP:(DE-MLZ)NOSPEC-20140101},
typ = {PUB:(DE-HGF)6},
url = {https://bib-pubdb1.desy.de/record/625360},
}