FNOs achieve polynomial sample complexity for learning time-T solution operators of dissipative evolution equations when those operators admit stable spectral discretizations, with rates depending on smoothness, dimension, and nonlinearity type.
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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
FNOs achieve polynomial sample complexity for learning time-T solution operators of dissipative evolution equations when those operators admit stable spectral discretizations, with rates depending on smoothness, dimension, and nonlinearity type.