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math.NA2025
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…
math.NA2025
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.…
math.NA2025
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…