Deep learning of nonlinear development of unstable flame fronts
(2023) MVKM01 20222Department 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:
http://lup.lub.lu.se/student-papers/record/9108878
- author
- Nobel, Ludvig LU
- supervisor
-
- Rixin Yu LU
- organization
- course
- MVKM01 20222
- year
- 2023
- 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}}, }