102 citations · 787 across the 61 of their papers we have counts for
5 papers · 2 filters
L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
Yanlai Chen, Lijie Ji, Akil Narayan +1
The task of repeatedly solving parametrized partial differential equations (pPDEs) in, e.g. optimization or interactive applications, makes it imperative to design highly efficient…
Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach
Ling Guo, Akil Narayan, Yongle Liu +1
One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about…
Structure-preserving function approximation via convex optimization
Vidhi Zala, Robert M. Kirby, Akil Narayan
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial a…
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve hyperbolicity of the original system. In this work, we develop hyper…
Analysis of The Ratio of and Norms in Compressed Sensing
Yiming Xu, Akil Narayan, Hoang Tran +1
We first propose a novel criterion that guarantees that an -sparse signal is the local minimizer of the objective; our criterion is interpretable and useful in p…