1 citations · 3 across the 8 of their papers we have counts for
8 papers
Integration of local and global surrogates for failure probability estimation
Audrey Gaymann, Juan M. Cardenas, Sung Min Jo +2
This paper presents the development of an algorithm, termed the Global-Local Hybrid Surrogate (GLHS), designed to efficiently compute the probability of rare failure events in comp…
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…
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…
A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity
Juan M. Cardenas, Manuel Solano
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximate…
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\…
Near-optimal sampling strategies for multivariate function approximation on general domains
Ben Adcock, Juan M. Cardenas
In this paper, we address the problem of approximating a multivariate function defined on a general domain in dimensions from sample points. We consider weighted least-squares…