11 papers
Numerical approximation of fractional diffusion equations on metric graphs
David Bolin, Lenin Riera-Segura, Alexandre B. Simas
We study fractional diffusion equations on compact metric graphs, where the nonlocal dynamics is governed by fractional powers of the shifted Kirchhoff-Laplacian. Building on recen…
Elliptic Bayesian Inverse Problems on Metric Graphs
David Bolin, Wenwen Li, Daniel Sanz-Alonso
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connect…
A new class of non-stationary Gaussian fields with general smoothness on metric graphs
David Bolin, Lenin Riera-Segura, Alexandre B. Simas
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivot…
A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework
David Bolin, Xiaotian Jin, Alexandre B. Simas +1
Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We int…
Whittle-Matérn Fields with Variable Smoothness
Hamza Ruzayqat, Wenyu Lei, David Bolin +2
We introduce and analyze a nonlocal generalization of Whittle--Matérn Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\u…
Fractional and Integer Order Sobolev Spaces for Compact Metric Graphs
Elsiddig Awadelkarim, David Bolin, Alexandre B. Simas
Given a compact metric graph and the Laplacian coupled with standard (Kirchhoff) vertex conditions, solutions to fractional elliptic partial differential equations of…