Author

Jakob Zech

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Preprint Oct 2026

Minimax Operator Learning for Holomorphic Maps between Hilbert Spaces

We consider the problem of learning nonlinear operators $G_0: \mathcal X\to \mathcal Y$ from finitely many noisy observations. While finite-regularity classes such as Lipschitz- or $C^k$-operators suffer from the curse of sample complexity (i.e. algebraic sample complexity is impossible), algebraic convergence rates ca...

Ly Duc Hoang, Sven Wang, Jakob Zech · 0 citations

Preprint Oct 2026

Bayesian Operator Learning: Posterior Existence and Convergence of Point Estimates for Gaussian Priors

We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map $g_0:\mathcal{X}\to\mathcal{Y}$ between separable Hilbert spaces, we study the recovery of $g_0$ from $n\in\mathbb{N}$ noisy input-output pairs $(\boldsymbol{X},\boldsymbol{Z})=(X_i,Z_i)_{i=1}^n$ with $Z_i=...

Niklas Reinhardt, Jakob Zech · 0 citations