67 citations · 109 across the 15 of their papers we have counts for
8 papers · 1 filter
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).…
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…
Analytic regularity and stochastic collocation of high dimensional Newton iterates
Julio Enrique Castrillon-Candas, Mark Kon
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In part…
Hybrid collocation perturbation for PDEs with random domains
Julio E. Castrillon-Candas, Fabio Nobile, Raul F. Tempone
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a rand…
A stochastic collocation approach for parabolic PDEs with random domain deformations
Julio E. Castrillon-Candas, Jie Xu
This work considers the problem of numerically approximating statistical moments of a Quantity of Interest (QoI) that depends on the solution of a linear parabolic partial differen…
Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
Julio E. Castrillon-Candas, Fabio Nobile, Raul F. Tempone
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a rand…
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
Julio Enrique Castrillon-Candas, Jun Li, Victor Eijkhout
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms…