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FMM-Net: neural network architecture based on the Fast Multipole Method

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arxiv 2212.12899 v1 pith:KP7LWJIB submitted 2022-12-25 math.NA cs.AIcs.LGcs.NA

Daria Sushnikova , Pavel Kharyuk , Ivan Oseledets This is my paper · ORCID
classification math.NAcs.AIcs.LGcs.NA
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In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.

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Cited by 1 Pith paper

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  1. MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs

    cs.CE 2025-07 conditional novelty 5.0 of 10

    The paper introduces MNO, an FMM-inspired neural operator that jointly maps PDE coefficients, source terms, and boundary conditions to the solution, and shows it works on 1D Poisson, Darcy flow, and a nonlinear BVP.

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