Parametric learning of time-advancement operators for unstable flame evolution
(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.
(Less)
- author
- Yu, Rixin LU and Hodzic, Erdzan LU
- organization
- publishing date
- 2024-04-01
- 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}}, }