133 citations · 198 across the 12 of their papers we have counts for
4 papers · 1 filter
A short tour of operator learning theory: Convergence rates, statistical limits, and open questions
Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical…
Extension and neural operator approximation of the electrical impedance tomography inverse map
Maarten V. de Hoop, Nikola B. Kovachki, Matti Lassas +1
This paper considers the problem of noise-robust neural operator approximation for the solution map of Calderón's inverse conductivity problem. In this continuum model of electrica…
Operator learning meets inverse problems: A probabilistic perspective
Nicholas H. Nelsen, Yunan Yang
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems…
The Random Feature Model for Input-Output Maps between Banach Spaces
Nicholas H. Nelsen, Andrew M. Stuart
Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approxim…