Sharp fractional Landau inequalities hold in rotating fractional Sobolev spaces for high-Mach compressible flows with explicit dependence on Mach number, rotation rate and anisotropy, yielding neural operator approximation rates of order N^{-ν/d_{α,Ω}}.
Nonlinear Approximation
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Explicit function classes are constructed where compositional approximation strictly outperforms superpositional approximation with arbitrarily large gaps.
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
A fixed-width, shared-activation deep network architecture is constructed so that every intermediate readout approximates the target function at a geometrically decaying rate proportional to depth.
A new fourth-order conservative adaptive multiresolution average-interpolating wavelet upwind scheme is proposed for hyperbolic conservation laws in compressible flows, using asymmetric wavelets for upwind discretization and symmetric ones for adaptation.
citing papers explorer
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Anisotropic Mixed Fractional Landau Inequalities for Rotating Compressible Flows
Sharp fractional Landau inequalities hold in rotating fractional Sobolev spaces for high-Mach compressible flows with explicit dependence on Mach number, rotation rate and anisotropy, yielding neural operator approximation rates of order N^{-ν/d_{α,Ω}}.
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Compositional Approximation Can Strictly Outperform Superpositional Approximation
Explicit function classes are constructed where compositional approximation strictly outperforms superpositional approximation with arbitrarily large gaps.
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Time-Frequency Analysis for Neural Networks
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
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Layer-wise Geometric Approximation Rates for Deep Networks
A fixed-width, shared-activation deep network architecture is constructed so that every intermediate readout approximates the target function at a geometrically decaying rate proportional to depth.
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A Fourth-order Conservative Adaptive Multiresolution Wavelet Upwind Scheme for Compressible Flows
A new fourth-order conservative adaptive multiresolution average-interpolating wavelet upwind scheme is proposed for hyperbolic conservation laws in compressible flows, using asymmetric wavelets for upwind discretization and symmetric ones for adaptation.