3 papers
math.AP2025
A 2-complex containing Sobolev spaces of matrix fields
Jay Gopalakrishnan, Kaibo Hu, Joachim Schöberl
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram…
math.NA2025
DPG loss functions for learning parameter-to-solution maps by neural networks
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of p…
physics.optics2025
Guided modes of helical waveguides
Jay Gopalakrishnan, Michael Neunteufel
This paper studies guided transverse scalar modes propagating through helically coiled waveguides. Modeling the modes as solutions of the Helmholtz equation within the three-dimens…