A conceptual argument that data-driven scientific models generalize outside their training data only when their mathematical form matches the true governing equation, which rules out neural operators and neural boundary-value models.
Operator learning with PCA-Net: upper and lower complexity bounds, October 2023
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From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
A conceptual argument that data-driven scientific models generalize outside their training data only when their mathematical form matches the true governing equation, which rules out neural operators and neural boundary-value models.