46 citations · 112 across the 16 of their papers we have counts for
10 papers · 1 filter
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…
The devil in the (de)tails: an improved recovery guarantee for sparse approximation
Ben Adcock, Simone Brugiapaglia, Avi Gupta
Many functions exhibit approximate sparsity in their coefficients with respect to a given dictionary. In recent literature, sparse approximation in such a dictionary from i.i.d. po…
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…
Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as com…
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…
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational…
Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit
Ben Adcock, Simone Brugiapaglia
We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension…
Correcting for unknown errors in sparse high-dimensional function approximation
Ben Adcock, Anyi Bao, Simone Brugiapaglia
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field c…
Compressed sensing approaches for polynomial approximation of high-dimensional functions
Ben Adcock, Simone Brugiapaglia, Clayton G. Webster
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of rece…
Recovery guarantees for compressed sensing with unknown errors
Simone Brugiapaglia, Ben Adcock, Richard K. Archibald
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarant…