---
_id: '67302'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Thorben
  full_name: Markmann, Thorben
  last_name: Markmann
- first_name: Michiel
  full_name: Straat, Michiel
  last_name: Straat
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Barbara
  full_name: Hammer, Barbara
  last_name: Hammer
citation:
  ama: Markmann T, Straat M, Peitz S, Hammer B. Fourier neural operators as data-driven
    surrogates for two- and three-dimensional Rayleigh–Bénard convection. <i>Neurocomputing</i>.
    2026;679:133201. doi:<a href="https://doi.org/10.1016/j.neucom.2026.133201">10.1016/j.neucom.2026.133201</a>
  apa: Markmann, T., Straat, M., Peitz, S., &#38; Hammer, B. (2026). Fourier neural
    operators as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard
    convection. <i>Neurocomputing</i>, <i>679</i>, 133201. <a href="https://doi.org/10.1016/j.neucom.2026.133201">https://doi.org/10.1016/j.neucom.2026.133201</a>
  bibtex: '@article{Markmann_Straat_Peitz_Hammer_2026, title={Fourier neural operators
    as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard convection},
    volume={679}, DOI={<a href="https://doi.org/10.1016/j.neucom.2026.133201">10.1016/j.neucom.2026.133201</a>},
    journal={Neurocomputing}, author={Markmann, Thorben and Straat, Michiel and Peitz,
    Sebastian and Hammer, Barbara}, year={2026}, pages={133201} }'
  chicago: 'Markmann, Thorben, Michiel Straat, Sebastian Peitz, and Barbara Hammer.
    “Fourier Neural Operators as Data-Driven Surrogates for Two- and Three-Dimensional
    Rayleigh–Bénard Convection.” <i>Neurocomputing</i> 679 (2026): 133201. <a href="https://doi.org/10.1016/j.neucom.2026.133201">https://doi.org/10.1016/j.neucom.2026.133201</a>.'
  ieee: 'T. Markmann, M. Straat, S. Peitz, and B. Hammer, “Fourier neural operators
    as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard convection,”
    <i>Neurocomputing</i>, vol. 679, p. 133201, 2026, doi: <a href="https://doi.org/10.1016/j.neucom.2026.133201">10.1016/j.neucom.2026.133201</a>.'
  mla: Markmann, Thorben, et al. “Fourier Neural Operators as Data-Driven Surrogates
    for Two- and Three-Dimensional Rayleigh–Bénard Convection.” <i>Neurocomputing</i>,
    vol. 679, 2026, p. 133201, doi:<a href="https://doi.org/10.1016/j.neucom.2026.133201">10.1016/j.neucom.2026.133201</a>.
  short: T. Markmann, M. Straat, S. Peitz, B. Hammer, Neurocomputing 679 (2026) 133201.
date_created: 2026-10-01T11:55:20Z
date_updated: 2026-10-01T11:56:04Z
department:
- _id: '655'
doi: 10.1016/j.neucom.2026.133201
intvolume: '       679'
keyword:
- own
- own-journal
- erc
language:
- iso: eng
page: '133201'
publication: Neurocomputing
publication_identifier:
  issn:
  - 0925-2312
status: public
title: Fourier neural operators as data-driven surrogates for two- and three-dimensional
  Rayleigh–Bénard convection
type: journal_article
user_id: '47427'
volume: 679
year: '2026'
...