Data-driven discovery of nonlinear wave equations in weak formulation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00387034" target="_blank" >RIV/68407700:21230/25:00387034 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.61782/fa.2025.0259" target="_blank" >http://dx.doi.org/10.61782/fa.2025.0259</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.61782/fa.2025.0259" target="_blank" >10.61782/fa.2025.0259</a>
Alternative languages
Result language
angličtina
Original language name
Data-driven discovery of nonlinear wave equations in weak formulation
Original language description
This paper deals with one of the subfields of physics-informed machine learning: data-driven discovery of partial differential equations. This work focuses on finite-amplitude sound propagation, i.e., nonlinear wave equations of the second-order approximation. Based on the principle of parsimony, we employ the sparsity promoting regression techniques to discover the governing equations. The training dataset was obtained by numerically solving the compressible Navier-Stokes equations. The investigated case involves the propagation of pressure pulses as travelling waves, leading to the discovery of the Westervelt equation. An algorithm trying to discover strong formulation of a partial differential equation suffers from low accuracy, due to the physical phenomena we are dealing with, i.e. local steep gradients. Improved accuracy was achieved when the problem is converted from strong formulation to a weak one. This benchmark study opens up opportunities for further discoveries in finite-amplitude sound propagation or findings linearizing transformations.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10307 - Acoustics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 11th Convention of the European Acoustics Association Forum Acusticum / EuroNoise 2025
ISBN
978-84-87985-35-5
ISSN
3005-7124
e-ISSN
3005-7124
Number of pages
5
Pages from-to
5269-5273
Publisher name
European Acoustics Association
Place of publication
Madrid
Event location
Malaga
Event date
Jun 23, 2025
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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