PRISM enables zero-shot parameterized high-dimensional high-order neural PDE solvers via implicit stochastic modulation that decouples parameters from the differentiation graph while preserving unbiased estimators.
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DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
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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Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers
PRISM enables zero-shot parameterized high-dimensional high-order neural PDE solvers via implicit stochastic modulation that decouples parameters from the differentiation graph while preserving unbiased estimators.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
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FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
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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.