6 citations · 17 across the 15 of their papers we have counts for
9 papers · 1 filter
Constructive Tchakaloff results and well-conditioned quadrature through randomized least squares
Filip Bělík, Akil Narayan, John Turnage
We consider using randomized least squares to construct quadrature rules exact on a subspace of functions. Using new conditions that we call relative admissibility and reference we…
Structure-Preserving Discontinuous Galerkin Methods for Stochastic Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. In many practical appl…
An Optimal Weighted Least-Squares Method for Operator Learning
John Turnage, Matthew Lowery, John Jakeman +3
We consider the problem of learning an unknown, possibly nonlinear operator between separable Hilbert spaces from supervised data. Inputs are drawn from a prescribed probability me…
Efficient and Robust Carathéodory-Steinitz Pruning of Positive Discrete Measures
Filip Bělík, Jesse Chan, Akil Narayan
In many applications, one seeks to approximate integration against a positive measure of interest by a positive discrete measure: a numerical quadrature rule with positive weights.…
Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods
Ray Qu, Akil Narayan, Jesse Chan
Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlin…
Energy Stable and Structure-Preserving Algorithms for the Stochastic Galerkin System of 2D Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering ph…
Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models
Ankur, Ram Jiwari, Akil Narayan
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixe…
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonline…
Certified reduced basis methods for fractional Laplace equations via extension
Harbir Antil, Yanlai Chen, Akil Narayan
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorith…