67 citations · 109 across the 15 of their papers we have counts for
16 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).…
deFOREST: Fusing Optical and Radar satellite data for Enhanced Sensing of Tree-loss
Julio Enrique Castrillon-Candas, Hanfeng Gu, Caleb Meredith +4
In this paper we develop a deforestation detection pipeline that incorporates optical and Synthetic Aperture Radar (SAR) data. A crucial component of the pipeline is the constructi…
Uncertainty quantification of receptor ligand binding sites prediction
Nanjie Chen, Dongliang Yu, Dmitri Beglov +2
Recent advancements in protein docking site prediction have highlighted the limitations of traditional rigid docking algorithms, like PIPER, which often neglect critical stochastic…
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…
Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection
Julio E Castrillon-Candas, Michael Rosenbaum, Mark Kon
Massive vector field datasets are common in multi-spectral optical and radar sensors, among many other emerging areas of application. We develop a novel stochastic functional (data…
Multilevel Stochastic Optimization for Imputation in Massive Medical Data Records
Wenrui Li, Xiaoyu Wang, Yuetian Sun +3
It has long been a recognized problem that many datasets contain significant levels of missing numerical data. A potentially critical predicate for application of machine learning…
Stochastic tensor space feature theory with applications to robust machine learning
Julio Enrique Castrillon-Candas, Kaili Shi, Dingning Liu +5
In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen--Loève feature theory based on stochastic tensor spaces, for the construction of robust machine learning fe…
Existence of Strong Solution for the Complexified Non-linear Poisson Boltzmann Equation
Brian Choi, Jie Xu, Trevor Norton +2
We prove the existence and uniqueness of the complexified Nonlinear Poisson-Boltzmann Equation (nPBE) in a bounded domain in . The nPBE is a model equation in nonline…
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…
Spatial best linear unbiased prediction: A computational mathematics approach for high dimensional massive datasets
Julio E. Castrillon-Candas
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. Howeve…
Multi-Level Restricted Maximum Likelihood Covariance Estimation and Kriging for Large Non-Gridded Spatial Datasets
Julio E. Castrillon-Candas, Marc G. Genton, Rio Yokota
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach pro…
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…