Neural operators approximate strongly continuous convex monotone semigroups
We approximate strongly continuous convex monotone semigroups by learning their Chernoff-type one-step operators with neural operators. First, we introduce the general class of so-called Chernoff-neural operators and show in a universal approximation theorem that they can approximate the Chernoff one-step operators arbitrarily well. By using stability estimates between weighted Hölder spaces, the one-step approximation error can be propagated through the iterations which yields universal approximation of the corresponding semigroup. Second, we introduce the more specialized class of envelope-neural operators for envelope semigroups which allows us to derive quantitative approximation rate...
| Authors | Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo |
|---|---|
| Primary category | math.NA |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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