795 citations · 1.4k across the 64 of their papers we have counts for
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CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions
Ben Adcock, Juan M. Cardenas, Nick Dexter
We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely poin…
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…
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…
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged…
The gap between theory and practice in function approximation with deep neural networks
Ben Adcock, Nick Dexter
Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-exp…
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems
Nina M. Gottschling, Vegard Antun, Anders C. Hansen +1
Methods inspired by Artificial Intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performances on challenging problem…
Convolutional Analysis Operator Learning: Dependence on Training Data
Il Yong Chun, David Hong, Ben Adcock +1
Convolutional analysis operator learning (CAOL) enables the unsupervised training of (hierarchical) convolutional sparsifying operators or autoencoders from large datasets. One can…