4 papers
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
Zachary Morrow, Michael Penwarden, Brian Chen +3
Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically…
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…