2 citations · 5 across the 8 of their papers we have counts for
10 papers
Into the danger zone: stable extrapolation in high-dimensional function and operator learning
Ben Adcock, Simone Brugiapaglia, Xuemeng Wang
Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the trainin…
Near-Optimal Learning of Gaussian Sobolev Operators
Ben Adcock, Michael Griebel, Gregor Maier
A key question in operator learning is how to design surrogate operators with provable approximation guarantees in reasonable computational time. Whereas smooth operators can be ap…
Fourier extensions for matrix-function block encodings with error-independent subnormalization bounds
Peter Brearley, Thomas L. Howarth, Ben Adcock
Block encodings of non-unitary matrix functions are central to quantum numerical linear algebra. Hamiltonian simulation is a natural input model for Hermitian matrices, but accurat…
Function recovery and optimal sampling in the presence of nonuniform evaluation costs
Ben Adcock
We consider recovering a function in an -dimensional linear subspace from i.i.d. pointwise samples via (weighted) least-squares esti…
The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
Ben Adcock, Michael Griebel, Gregor Maier
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Oper…
Optimal sampling for least-squares approximation
Ben Adcock
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is…
Optimal deep learning of holomorphic operators between Banach spaces
Ben Adcock, Nick Dexter, Sebastian Moraga
Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the op…
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in…
A unified framework for learning with nonlinear model classes from arbitrary linear samples
Ben Adcock, Juan M. Cardenas, Nick Dexter
We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hil…
Monte Carlo is a good sampling strategy for polynomial approximation in high dimensions
Ben Adcock, Simone Brugiapaglia
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computationa…