Neural operators approximate strongly continuous convex monotone semigroups

• URL: http://arxiv.org/abs/2609.02727v1
• Date: Wed, 02 Sep 2026 15:38:52 GMT
• Title: Neural operators approximate strongly continuous convex monotone semigroups
• Abstract summary: We approximate strongly continuous monotone convex semigroups by learning their Chernoff-type one-step operators with neural operators.<n>We show in a universal approximation theorem that they can approximate the Chernoff one-step operators arbitrarily well.
• Score: 41.99844472131922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 rates. Finally, we illustrate the effectiveness of these neural operators in several numerical examples arising from non-linear partial differential equations, stochastic optimal control and stochastic processes under model uncertainty.

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