4 papers
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).…
Off-Centered WoS-Type Solvers with Statistical Weighting
Anchang Bao, Jie Xu, Enya Shen +1
Stochastic PDE solvers have emerged as a powerful alternative to traditional discretization-based methods for solving partial differential equations (PDEs), especially in geometry…
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…
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…