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Enhancement of shock-capturing methods via machine learning

Stevens, Ben and Colonius, Tim (2020) Enhancement of shock-capturing methods via machine learning. Theoretical and Computational Fluid Dynamics, 34 (4). pp. 483-496. ISSN 0935-4964. https://resolver.caltech.edu/CaltechAUTHORS:20200526-131556031

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Abstract

In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgers’ equation, and the 1-D Euler equations. For the latter, we examine the Shu–Osher model problem for turbulence–shock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00162-020-00531-1DOIArticle
https://arxiv.org/abs/2002.02521arXivDiscussion Paper
ORCID:
AuthorORCID
Stevens, Ben0000-0002-3410-5922
Colonius, Tim0000-0003-0326-3909
Additional Information:© 202 Springer. Received 31 October 2019; Accepted 21 April 2020; Published 23 May 2020. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1745301. The authors declare that they have no conflict of interest.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1745301
Subject Keywords:Shock capturing; Machine learning; Fluid mechanics
Issue or Number:4
Record Number:CaltechAUTHORS:20200526-131556031
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200526-131556031
Official Citation:Stevens, B., Colonius, T. Enhancement of shock-capturing methods via machine learning. Theor. Comput. Fluid Dyn. 34, 483–496 (2020). https://doi.org/10.1007/s00162-020-00531-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103457
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 May 2020 20:23
Last Modified:25 Aug 2020 17:36

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