Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

Deep learning of nonlinear development of unstable flame fronts

Nobel, Ludvig LU (2023) MVKM01 20222
Department of Energy Sciences
Abstract
The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. From the generated solution functions an operator is trained to map the function to a future solution function after a small time-step. The goal is for this operator to be able to accurately map long sequences of solutions through repeated application of the operator. Two networks were trained for this task, a Convolutional Neural Network and... (More)
The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. From the generated solution functions an operator is trained to map the function to a future solution function after a small time-step. The goal is for this operator to be able to accurately map long sequences of solutions through repeated application of the operator. Two networks were trained for this task, a Convolutional Neural Network and A Fourier Neural Operator. The investigation found that the operator were not only able to accurately predict fairly long
sequences, but was also able to capture the long-term characteristics of the flame front development. This study also shows that it is possible with specific modifications to a Convolutional Neural Network proposed in the study, a single Neural Network is able to make accurate recurrent predictions for multiple values of a parameter affecting the solution of the partial differential equation considered. (Less)
Please use this url to cite or link to this publication:
author
Nobel, Ludvig LU
supervisor
organization
course
MVKM01 20222
year
type
H2 - Master's Degree (Two Years)
subject
report number
LUTMDN/TMHP-23/5515-SE
ISSN
0282-1990
language
English
id
9108878
date added to LUP
2023-01-31 10:41:36
date last changed
2023-01-31 10:41:36
@misc{9108878,
  abstract     = {{The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. From the generated solution functions an operator is trained to map the function to a future solution function after a small time-step. The goal is for this operator to be able to accurately map long sequences of solutions through repeated application of the operator. Two networks were trained for this task, a Convolutional Neural Network and A Fourier Neural Operator. The investigation found that the operator were not only able to accurately predict fairly long
sequences, but was also able to capture the long-term characteristics of the flame front development. This study also shows that it is possible with specific modifications to a Convolutional Neural Network proposed in the study, a single Neural Network is able to make accurate recurrent predictions for multiple values of a parameter affecting the solution of the partial differential equation considered.}},
  author       = {{Nobel, Ludvig}},
  issn         = {{0282-1990}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Deep learning of nonlinear development of unstable flame fronts}},
  year         = {{2023}},
}