9 papers
Efficient and Robust Carathéodory-Steinitz Pruning of Positive Discrete Measures
Filip BÄlÃk, 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.…
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…
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…
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…
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…