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math.ST2026
Bayesian Operator Learning: Posterior Existence and Convergence of Point Estimates for Gaussian Priors
Niklas Reinhardt, Jakob Zech
We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map between separable Hilbert spaces,…
math.ST2024
Statistical Learning Theory for Neural Operators
Niklas Reinhardt, Sven Wang, Jakob Zech
We present statistical convergence results for the learning of (possibly) non-linear mappings in infinite-dimensional spaces. Specifically, given a map $G_0:\mathcal X\to\mathcal Y…