5 citations · 10 across the 9 of their papers we have counts for
9 papers
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…
Optimal approximation of infinite-dimensional holomorphic functions II: recovery from i.i.d. pointwise samples
Ben Adcock, Nick Dexter, Sebastian Moraga
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational…
Optimal approximation of infinite-dimensional holomorphic functions
Ben Adcock, Nick Dexter, Sebastian Moraga
Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computatio…
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…
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…
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…
Sample Size Considerations for Bayesian Multilevel Hidden Markov Models: A Simulation Study on Multivariate Continuous Data with highly overlapping Component Distributions based on Sleep Data
Jasper Ginn, Sebastian Mildiner Moraga, Emmeke Aarts
Spurred in part by the ever-growing number of sensors and web-based methods of collecting data, the use of Intensive Longitudinal Data (ILD) is becoming more common in the social a…
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…