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Koopman theory-inspired method for learning time advancement operators in unstable flame front evolution

Yu, Rixin LU orcid ; Herbert, Marco ; Klein, Markus and Hodzic, Erdzan LU (2025) In Physics of Fluids 37(2).
Abstract

Predicting the evolution of complex systems governed by partial differential equations remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier neural operators and convolutional neural networks to learn solution advancement operators for flame front instabilities. By transforming data into a high-dimensional latent space, these models achieve more accurate multi-step predictions compared to traditional methods. Benchmarking across one- and two-dimensional flame front scenarios demonstrates the proposed approaches' superior performance in short-term accuracy and long-term statistical reproduction, offering a promising framework for modeling complex dynamical 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
in
Physics of Fluids
volume
37
issue
2
article number
024115
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:85217915853
ISSN
1070-6631
DOI
10.1063/5.0252716
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 Author(s).
id
bbd3b4e4-d785-4ef0-83d6-24e6115e0ec1
date added to LUP
2025-06-23 14:32:16
date last changed
2025-10-14 11:13:14
@article{bbd3b4e4-d785-4ef0-83d6-24e6115e0ec1,
  abstract     = {{<p>Predicting the evolution of complex systems governed by partial differential equations remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier neural operators and convolutional neural networks to learn solution advancement operators for flame front instabilities. By transforming data into a high-dimensional latent space, these models achieve more accurate multi-step predictions compared to traditional methods. Benchmarking across one- and two-dimensional flame front scenarios demonstrates the proposed approaches' superior performance in short-term accuracy and long-term statistical reproduction, offering a promising framework for modeling complex dynamical systems.</p>}},
  author       = {{Yu, Rixin and Herbert, Marco and Klein, Markus and Hodzic, Erdzan}},
  issn         = {{1070-6631}},
  language     = {{eng}},
  month        = {{02}},
  number       = {{2}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Physics of Fluids}},
  title        = {{Koopman theory-inspired method for learning time advancement operators in unstable flame front evolution}},
  url          = {{http://dx.doi.org/10.1063/5.0252716}},
  doi          = {{10.1063/5.0252716}},
  volume       = {{37}},
  year         = {{2025}},
}