102 citations · 787 across the 61 of their papers we have counts for
10 papers · 2 filters
GP-HMAT: Scalable, Gaussian Process Regression with Hierarchical Low-Rank Matrices
Vahid Keshavarzzadeh, Shandian Zhe, Robert M. Kirby +1
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationshi…
Structure-preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods
Vidhi Zala, Robert M. Kirby, Akil Narayan
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized…
Adaptive Density Tracking by Quadrature for Stochastic Differential Equations
Ryleigh A. Moore, Akil Narayan
Density tracking by quadrature (DTQ) is a numerical procedure for computing solutions to Fokker-Planck equations that describe probability densities for stochastic differential equ…
Optimal design for kernel interpolation: applications to uncertainty quantification
Akil Narayan, Liang Yan, Tao Zhou
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation us…
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
Stochastic Galerkin formulations of the two-dimensional shallow water systems parameterized with random variables may lose hyperbolicity, and hence change the nature of the origina…
A bandit-learning approach to multifidelity approximation
Yiming Xu, Vahid Keshavarzzadeh, Robert M. Kirby +1
Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varyin…