15 citations · 63 across the 20 of their papers we have counts for
9 papers · 1 filter
Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials
Jorge Suzuki, Mamikon Gulian, Mohsen Zayernouri +1
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, du…
On the fractional Laplacian of variable order
Eric Darve, Marta D'Elia, Roberto Garrappa +2
We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the…
Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport
Marta D'Elia, Mamikon Gulian
We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators i…
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Guofei Pang, Marta D'Elia, Michael Parks +1
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity…
An energy-based coupling approach to nonlocal interface problems
Giacomo Capodaglio, Marta D'Elia, Pavel Bochev +1
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations…
A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
Marta D'Elia, Xingjie Li, Pablo Seleson +2
Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. T…