Showing math.NAShow all
3 papers · 1 filter
math.NA2026
The Segal-Bargmann Transform in Neural Partial Differential Equations
Jie Xu, Julio Castrillón-Candás, Mark Kon +1
We introduce a novel neural operator method based on Segal-Bargmann transform and Bargmann-Fock space for learning the solution operators of partial differential equations (PDEs).…
math.NA2023
Uncertainty quantification and complex analyticity of the nonlinear Poisson-Boltzmann equation for the interface problem with random domains
Trevor Norton, Jie Xu, Brian Choi +2
The nonlinear Poisson-Boltzmann equation (NPBE) is an elliptic partial differential equation used in applications such as protein interactions and biophysical chemistry (among many…
math.NA2023
Analytic regularity of strong solutions for the complexified stochastic non-linear Poisson Boltzmann Equation
Brian Choi, Jie Xu, Trevor Norton +2
Semi-linear elliptic Partial Differential Equations (PDEs) such as the non-linear Poisson Boltzmann Equation (nPBE) is highly relevant for non-linear electrostatics in computationa…