---
res:
  bibo_abstract:
  - Data-driven surrogate models provide fast and fully differentiable approximations
    of complex dynamical systems. In this work, we develop such surrogates for the
    Rayleigh–Bénard convection (RBC), which governs thermally driven flows in natural
    and industrial environments. Specifically, the proposed models approximate the
    discrete-time flow map of the RBC system, advancing the full system state by a
    fixed time step. We train Fourier Neural Operator (FNO)–based models to learn
    the dynamics of RBC in two and three dimensions and compare them to a convolutional
    U-Net baseline and a Koopman-based Linear Recurrent Autoencoder Network (LRAN).
    The two-dimensional system serves as a baseline for the more challenging three-dimensional
    case, which exhibits increased spatial complexity and turbulent dynamics. Across
    all settings, FNO-based models consistently outperform the LRAN, while achieving
    performance comparable to the U-Net in several regimes. Incorporating spatio-temporal
    inputs via FNOs leads to improved long-term prediction accuracy, particularly
    for turbulent flows. The physical fidelity of the predictions is assessed using
    convective heat flux statistics, profiles, and fluctuations, showing that FNOs
    most closely reproduce the ground-truth flow statistics. In addition, we demonstrate
    that FNOs enable zero-shot super-resolution across unseen spatial discretizations,
    a capability not shared by the convolutional baselines. These results highlight
    the potential of neural operator–based models as accurate, physically consistent,
    and resolution-independent surrogates for downstream tasks such as flow control.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Thorben
      foaf_name: Markmann, Thorben
      foaf_surname: Markmann
  - foaf_Person:
      foaf_givenName: Michiel
      foaf_name: Straat, Michiel
      foaf_surname: Straat
  - foaf_Person:
      foaf_givenName: Sebastian
      foaf_name: Peitz, Sebastian
      foaf_surname: Peitz
      foaf_workInfoHomepage: http://www.librecat.org/personId=47427
    orcid: 0000-0002-3389-793X
  - foaf_Person:
      foaf_givenName: Barbara
      foaf_name: Hammer, Barbara
      foaf_surname: Hammer
  bibo_doi: 10.1016/j.neucom.2026.133201
  bibo_volume: 679
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0925-2312
  dct_language: eng
  dct_subject:
  - own
  - own-journal
  - erc
  dct_title: Fourier neural operators as data-driven surrogates for two- and three-dimensional
    Rayleigh–Bénard convection@
...