180 citations · 1.1k across the 26 of their papers we have counts for
13 papers · 1 filter
Deep learning of parameterized equations with applications to uncertainty quantification
Tong Qin, Zhen Chen, John Jakeman +1
We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the r…
Adaptive Multi-index Collocation for Uncertainty Quantification and Sensitivity Analysis
John D. Jakeman, Michael Eldred, Gianluca Geraci +1
In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is ba…
Polynomial chaos expansions for dependent random variables
John Jakeman, Fabian Franzelin, Akil Narayan +2
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple…
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification
T. Butler, J. D. Jakeman, T. Wildey
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantif…
Generation and application of multivariate polynomial quadrature rules
John D. Jakeman, Akil Narayan
The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate…
A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures
T. Butler, J. D. Jakeman, T. Wildey
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of int…
Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations
Ben Adcock, Anyi Bao, John D. Jakeman +1
The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, re…
A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions
John D. Jakeman, Akil Narayan, Tao Zhou
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomi…
A Christoffel function weighted least squares algorithm for collocation approximations
Akil Narayan, John D. Jakeman, Tao Zhou
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame-…
Enhancing -minimization estimates of polynomial chaos expansions using basis selection
John D. Jakeman, Michael S. Eldred, Khachik Sargsyan
In this paper we present a basis selection method that can be used with -minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). T…
Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates
John D. Jakeman, Timothy Wildey
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-bas…
Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation
Akil Narayan, John Jakeman
We propose an adaptive sparse grid stochastic collocation approach based upon Leja interpolation sequences for approximation of parameterized functions with high-dimensional parame…
Local and Dimension Adaptive Sparse Grid Interpolation and Quadrature
John D. Jakeman, Stephen G. Roberts
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algo…