795 citations · 1.4k across the 64 of their papers we have counts for
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Stable and accurate least squares radial basis function approximations on bounded domains
Ben Adcock, Daan Huybrechs, Cécile Piret
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-condition…
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…
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning
Ben Adcock, Juan M. Cardenas, Nick Dexter
The problem of approximating smooth, multivariate functions from sample points arises in many applications in scientific computing, e.g., in computational Uncertainty Quantificatio…
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…
NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems
Maksym Neyra-Nesterenko, Ben Adcock
Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to ou…
Towards optimal sampling for learning sparse approximation in high dimensions
Ben Adcock, Juan M. Cardenas, Nick Dexter +1
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert…
An Adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains
Ben Adcock, Juan M. Cardenas, Nick Dexter
Many problems in computational science and engineering can be described in terms of approximating a smooth function of variables, defined over an unknown domain of interest $Ω\…