Operator approximation of the wave equation based on deep learning of Green's function

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior knowledge about the solution structure of a problem and can th...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2024-04, Vol.159, p.21-30
Main Authors: Aldirany, Ziad, Cottereau, Régis, Laforest, Marc, Prudhomme, Serge
Format: Article
Language:English
Subjects:
Computer Science
Deep learning
Deep operator networks
Fundamental solution
Green's function
Modeling and Simulation
Physics-informed neural networks
Wave equation
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Summary:Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior knowledge about the solution structure of a problem and can thus be directly applied to a large class of problems. However, training the parameters of the networks may sometimes be slow. In order to improve on DeepONets for approximating the wave equation, we introduce the Green operator networks (GreenONets), which use the representation of the exact solution to the homogeneous wave equation in term of the Green's function. The performance of GreenONets and DeepONets is compared on a series of numerical experiments for homogeneous and heterogeneous media in one and two dimensions.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2024.01.018