arXiv Machine Learning By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu

Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

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arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.

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arXiv Machine Learning
1d ago

Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation

The paper presents Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a new approach to solving the Helmholtz equation. By decomposing the computational domain into overlapping sub‑domains, each governed by a local neural network, the method aims to improve accuracy and computational efficiency for high‑frequency wave problems in complex two‑dimensional domains. The authors evaluate the technique on the homogeneous Helmholtz case, showing its potential to overcome limitations of traditional finite difference and finite element methods.

By Victorita Dolean, Daria Hrebenshchykova, St\'ephane Lanteri, Victor Michel-Dansac