Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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Conditional KRR reduces to KRR on a residual kernel with an added O(1/sqrt(N)) term in expected test risk and outperforms standard KRR when the F-component is dominant.
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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Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows
Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding
Conditional KRR reduces to KRR on a residual kernel with an added O(1/sqrt(N)) term in expected test risk and outperforms standard KRR when the F-component is dominant.
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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.