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Neural operators show promise in approximating complex mathematical semigroups

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a novel approach using neural operators to approximate strongly continuous convex monotone semigroups. The study introduces Chernoff-neural operators, demonstrating their universal approximation capabilities for Chernoff one-step operators. By leveraging stability estimates, the approximation error of these one-step operators can be propagated to approximate the corresponding semigroup. Additionally, envelope-neural operators are presented for envelope semigroups, enabling quantitative approximation rates. These methods have shown effectiveness in numerical examples related to nonlinear partial differential equations, stochastic optimal control, and stochastic processes under model uncertainty. AI

IMPACT This research could lead to more efficient numerical methods for solving complex differential equations and stochastic processes.

RANK_REASON The item is an academic paper published on arXiv detailing a new mathematical approximation technique. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Neural operators show promise in approximating complex mathematical semigroups

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The item is an academic paper published on arXiv detailing a new mathematical approximation technique. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo ·

    Neural operators approximate strongly continuous convex monotone semigroups

    arXiv:2609.02727v1 Announce Type: cross 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 uni…

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