@article{2efc2126-9cf8-4a8e-9dee-37ae2ff1eef6,
  abstract     = {{<p>We introduce the Koopman-inspired Fourier Neural Operator (kFNO) for predicting complex flame instabilities governed by nonlinear PDEs. Leveraging Koopman theory to lift dynamics into a high-dimensional latent space, kFNO improves short-term accuracy and long-term statistical fidelity. We validate kFNO on synthesized flame fronts from re-scaled Sivashinsky equations (modeling hybrid Darrieus–Landau and Diffusive-Thermal instabilities) and on large-scale DNS data of DL-unstable flames. Compared to the baseline FNO, kFNO achieves 2–6 times lower errors, more accurate dispersion relations, and superior computational efficiency, demonstrating its promise for efficient operator learning in chaotic, high-dimensional systems.</p>}},
  author       = {{Yu, Rixin and Herbert, Marco and Klein, Markus and Hodzic, Erdzan}},
  issn         = {{0045-7930}},
  keywords     = {{Chaotic dynamics; Darrieus–Landau instability; Diffusive Thermal instability; Flame instabilities; Fourier neural operator; Koopman operator; Operator learning; PDE learning; Sivashinsky equation}},
  language     = {{eng}},
  month        = {{08}},
  publisher    = {{Elsevier}},
  series       = {{Computers and Fluids}},
  title        = {{Koopman-inspired operator learning for intrinsic flame instabilities}},
  url          = {{http://dx.doi.org/10.1016/j.compfluid.2026.107165}},
  doi          = {{10.1016/j.compfluid.2026.107165}},
  volume       = {{317}},
  year         = {{2026}},
}