A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
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Pith papers citing it
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math.NA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
IV-Net is a multigrid-inspired convolutional neural operator that approximates solutions to linear elliptic PDEs with high-contrast coefficients and shows better accuracy than POD and other neural operators on heterogeneous coercive problems.
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Solving Convolution-type Integral Equations using Preconditioned Neural Operators
A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
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IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients
IV-Net is a multigrid-inspired convolutional neural operator that approximates solutions to linear elliptic PDEs with high-contrast coefficients and shows better accuracy than POD and other neural operators on heterogeneous coercive problems.