Neural operators approximate strongly continuous convex monotone semigroups
Read the original on arXiv Machine Learning →The paper introduces Chernoff-neural operators, a class of neural operators that can universally approximate Chernoff-type one-step operators for strongly continuous convex monotone semigroups. A universal approximation theorem is proved, and stability estimates in weighted Hölder spaces allow the one-step error to propagate, yielding universal approximation of the entire semigroup. The authors also define envelope-neural operators for envelope semigroups, providing quantitative approximation rates, and demonstrate the approach on numerical examples from nonlinear PDEs, stochastic optimal control, and uncertain stochastic processes.
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