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Parametric learning of time-advancement operators for unstable flame evolution

Yu, Rixin LU and Hodzic, Erdzan LU (2024) In Physics of Fluids 36(4).
Abstract

This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning... (More)

This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physics of Fluids
volume
36
issue
4
article number
044109
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:85190065876
ISSN
1070-6631
DOI
10.1063/5.0203546
language
English
LU publication?
yes
id
f2ed4c64-59ec-4482-8ac9-16ebbcc55d92
date added to LUP
2024-04-24 14:51:42
date last changed
2024-04-24 14:52:51
@article{f2ed4c64-59ec-4482-8ac9-16ebbcc55d92,
  abstract     = {{<p>This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.</p>}},
  author       = {{Yu, Rixin and Hodzic, Erdzan}},
  issn         = {{1070-6631}},
  language     = {{eng}},
  month        = {{04}},
  number       = {{4}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Physics of Fluids}},
  title        = {{Parametric learning of time-advancement operators for unstable flame evolution}},
  url          = {{http://dx.doi.org/10.1063/5.0203546}},
  doi          = {{10.1063/5.0203546}},
  volume       = {{36}},
  year         = {{2024}},
}