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.
FMM-Net: neural network architecture based on the Fast Multipole Method
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abstract
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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MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs
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.