6 citations · 17 across the 15 of their papers we have counts for
15 papers
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…
SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation
Zachary Morrow, Michael Penwarden, Brian Chen +3
Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are flexible function approximators, but their accuracy can require substantial network depth, width, and trainabl…
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.…
Hybrid least squares for learning functions from highly noisy data
Ben Adcock, Bernhard Hientzsch, Akil Narayan +1
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods…
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…
Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation
Da Long, Zhitong Xu, Guang Yang +2
Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine lea…
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
Matthew Lowery, John Turnage, Zachary Morrow +4
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for…
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…
Multi-Resolution Active Learning of Fourier Neural Operators
Shibo Li, Xin Yu, Wei Xing +3
Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and p…
Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks
Shibo Li, Michael Penwarden, Yiming Xu +4
Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, apply differen…
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…