17 citations · 35 across the 9 of their papers we have counts for
12 papers
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…
Probabilistic partition of unity networks: clustering based deep approximation
Nat Trask, Mamikon Gulian, Andy Huang +1
Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of trainin…
Distribution and pressure of active Lévy swimmers under confinement
Tingtao Zhou, Zhiwei Peng, Mamikon Gulian +1
Many active matter systems are known to perform Lévy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patt…
Partition of unity networks: deep hp-approximation
Kookjin Lee, Nathaniel A. Trask, Ravi G. Patel +2
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity…
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…
Gaussian Process Regression constrained by Boundary Value Problems
Mamikon Gulian, Ari Frankel, Laura Swiler
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value p…