Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.
arXiv preprint arXiv:2006.09535 , year =
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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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Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.
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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.