Attention-based hybrid solvers for linear equations that are geometry aware

Idan Versano; Eli Turkel

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arXiv · 2411.13341

Attention-based hybrid solvers for linear equations that are geometry aware

Idan Versano·Eli Turkel

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Abstract

We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust preconditioner for problems defined by different geometries without further fine-tuning or additional data mining. We demonstrate our method for the Helmholtz equation, which is used to solve problems in electromagnetics and acoustics; the Helmholtz equation is not positive definite, and with absorbing boundary conditions, it is not symmetric.

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Idan Versano, Eli Turkel. 2024-11-20. Attention-based hybrid solvers for linear equations that are geometry aware. https://arxiv.org/abs/2411.13341

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