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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},
}