120 citations · 178 across the 21 of their papers we have counts for
21 papers
Active Learning for Conditional Generative Compressed Sensing
Alexander DeLise, Nick Dexter
Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional vers…
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…
Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics
Simone Brugiapaglia, Nick Dexter, Samir Karam +1
On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Different…
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…
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…
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…
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…
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…
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\…
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…
Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging
Ben Adcock, Nick Dexter, Qinghong Xu
In this paper, we consider the use of Total Variation (TV) minimization for compressive imaging; that is, image reconstruction from subsampled measurements. Focusing on two importa…
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…
Reconstructing high-dimensional Hilbert-valued functions via compressed sensing
Nick Dexter, Hoang Tran, Clayton Webster
We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equat…
A mixed regularization approach for sparse simultaneous approximation of parameterized PDEs
Nick Dexter, Hoang Tran, Clayton Webster
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochast…
On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals
Nick Dexter, Hoang Tran, Clayton Webster
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in cont…
Polynomial approximation via compressed sensing of high-dimensional functions on lower sets
Abdellah Chkifa, Nick Dexter, Hoang Tran +1
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting wher…
Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients
Nick Dexter, Clayton Webster, Guannan Zhang
This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM) for approximating the solution of parameterized elliptic partial di…