3 citations · 4 across the 5 of their papers we have counts for
7 papers
Minimax Operator Learning for Holomorphic Maps between Hilbert Spaces
Ly Duc Hoang, Sven Wang, Jakob Zech
We consider the problem of learning nonlinear operators from finitely many noisy observations. While finite-regularity classes such as Lipschitz- or…
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,…
Optimal Scheduling of Dynamic Transport
Panos Tsimpos, Zhi Ren, Jakob Zech +1
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measur…
Low Stein Discrepancy via Message-Passing Monte Carlo
Nathan Kirk, T. Konstantin Rusch, Jakob Zech +1
Message-Passing Monte Carlo (MPMC) was recently introduced as a novel low-discrepancy sampling approach leveraging tools from geometric deep learning. While originally designed for…
Distribution learning via neural differential equations: minimal energy regularization and approximation theory
Youssef Marzouk, Zhi Ren, Jakob Zech
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g…
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…
Distribution learning via neural differential equations: a nonparametric statistical perspective
Youssef Marzouk, Zhi Ren, Sven Wang +1
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex…