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Koopman-inspired operator learning for intrinsic flame instabilities

Yu, Rixin LU orcid ; Herbert, Marco ; Klein, Markus and Hodzic, Erdzan LU (2026) In Computers and Fluids 317.
Abstract

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.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Chaotic dynamics, Darrieus–Landau instability, Diffusive Thermal instability, Flame instabilities, Fourier neural operator, Koopman operator, Operator learning, PDE learning, Sivashinsky equation
in
Computers and Fluids
volume
317
article number
107165
publisher
Elsevier
external identifiers
  • scopus:105040686355
ISSN
0045-7930
DOI
10.1016/j.compfluid.2026.107165
project
Advancing Fluid Simulations with AI: Physics-Informed Neural Networks (AI Lund initiate)
Deep learing of LES combusiton model
language
English
LU publication?
yes
id
2efc2126-9cf8-4a8e-9dee-37ae2ff1eef6
date added to LUP
2026-06-16 20:37:15
date last changed
2026-08-17 09:46:49
@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}},
}