Neural operators approximate continuous operators from H^s to H^t with O(N^{-s/d}) error in H^t norm; FNOs on Burgers achieve H^1 errors to 10^{-7} and follow a power-law scaling with exponent ~1.4.
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Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
Neural operators approximate continuous operators from H^s to H^t with O(N^{-s/d}) error in H^t norm; FNOs on Burgers achieve H^1 errors to 10^{-7} and follow a power-law scaling with exponent ~1.4.