34 citations · 162 across the 24 of their papers we have counts for
5 papers · 1 filter
The Parametric Complexity of Operator Learning
Samuel Lanthaler, Andrew M. Stuart
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emula…
Neural Oscillators are Universal
Samuel Lanthaler, T. Konstantin Rusch, Siddhartha Mishra
Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physica…
Error Bounds for Learning with Vector-Valued Random Features
Samuel Lanthaler, Nicholas H. Nelsen
This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-…
Nonlocality and Nonlinearity Implies Universality in Operator Learning
Samuel Lanthaler, Zongyi Li, Andrew M. Stuart
Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engin…
Operator learning with PCA-Net: upper and lower complexity bounds
Samuel Lanthaler
PCA-Net is a recently proposed neural operator architecture which combines principal component analysis (PCA) with neural networks to approximate operators between infinite-dimensi…