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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Presents DHPO and a pretrained DeepONet inverse modeling framework that discovers unknown PDE terms and infers parameters across equation families with O(10^-2) solution and O(10^-3) parameter errors on benchmarks.
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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.
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Learning Hidden Physics and System Parameters with Deep Operator Networks
Presents DHPO and a pretrained DeepONet inverse modeling framework that discovers unknown PDE terms and infers parameters across equation families with O(10^-2) solution and O(10^-3) parameter errors on benchmarks.