Author

Philipp Schmocker

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Jul 2026

NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

NeuralChaos -- a neural operator architecture that produces elements of $\mathcal{H}^2_T(\mathbb{R}^{d})$ using only finitely many evaluations of the driving Brownian motion, while preserving predictability and square-integrability is introduced.

Anastasis Kratsios, Giulia Livieri, Philipp Schmocker · arXiv.org · 1 citation

#machine learning Preprint Sep 2026

Neural operators approximate strongly continuous convex monotone semigroups

This work introduces the general class of so-called Chernoff-neural operators and shows in a universal approximation theorem that they can approximate the Chernoff one-step operators arbitrarily well, and introduces the more specialized class of envelope-neural operators for envelope semigroups which allows for quantit...

Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo · 0 citations