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This paper provides approximation and generalization error estimates for multi-input neural operators measured in Sobolev norms, analyzing how multiple input functions with different domains and regularities affect error bounds, applicable to PDE and scientific computing problems.
This paper establishes quantitative Sobolev approximation bounds for neural operators, proving that operators can be uniformly approximated with explicit complexity-error relations. It validates these theoretical bounds using Fourier Neural Operators on the Burgers' equation, demonstrating that Sobolev-space approximation theory accurately predicts scaling behavior.
This paper introduces the Online Shared Supply Allocation problem and proposes a deterministic threshold-proportional policy (GPA) that achieves a 4/3-approximation to the offline optimum. It also includes a learning-augmented extension to handle imperfect forecasts and demonstrates superior performance in synthetic and real-world experiments.