Neural operators that are diffeomorphisms generally cannot be continuously discretized, but strongly monotone neural operators can, and bilipschitz neural operators decompose into strongly monotone layers plus a single isometry.
Neural operator: Learning maps between function spaces with applications to pdes
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Can neural operators always be continuously discretized?
Neural operators that are diffeomorphisms generally cannot be continuously discretized, but strongly monotone neural operators can, and bilipschitz neural operators decompose into strongly monotone layers plus a single isometry.