1 citations · 3 across the 8 of their papers we have counts for
9 papers
Variationally correct loss functions for nonlinear parametric problems and their neural approximations
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We construct computable a posteriori error estimators for parametric families of nonlinear elliptic problems by measuring the residual of a variational formulation in the dual norm…
Sufficient conditions for QMC analysis of finite elements for parametric differential equations
Vesa Kaarnioja, Andreas Rupp, Jay Gopalakrishnan
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown…
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…
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…
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…
The Johnson-Krizek-Mercier elasticity element in any dimensions
Jay Gopalakrishnan, Johnny Guzman, Jeonghun J. Lee
Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components wi…
On the improved convergence of lifted distributional Gauss curvature from Regge elements
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to…
Generalizing Riemann curvature to Regge metrics
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components…
PT-symmetry enabled stable modes in multi-core fiber
Tamara Gratcheva, Yogesh N. Joglekar, Jay Gopalakrishnan
Open systems with balanced gain and loss, described by parity-time PT-symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite…