mlsanityData to 7 Oct 2026

BENO: Boundary-embedded Neural Operators for Elliptic PDEs

arXiv 2401.09323 ↗First posted 17 Jan 2024cs.LGcited by 22

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Abstract (arXiv)

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 27 of its 47 references that are in the map. First posted on arXiv 17 Jan 2024.

Builds on

27 of 47 references.

References · 27

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15 more
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  6. 2026Generalized Neural Operator for Parametric and Boundary-Value Problemscited by 0
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