Data-driven discovery of nonlinear wave equations in weak formulation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Data-driven discovery of nonlinear wave equations in weak formulation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Data-driven discovery of nonlinear wave equations in weak formulation

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10307 - Acoustics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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

Počet stran výsledku

5

Strana od-do

5269-5273

Název nakladatele

European Acoustics Association

Místo vydání

Madrid

Místo konání akce

Malaga

Datum konání akce

23. 6. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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