4 papers · 1 filter
Entropy Analysis of some Active Scalar Equations
Elie Abdo
We study a broad family of active scalar equations with fractional dissipation on and prove that their entropy diverges to at a sharp rate of order $\log t…
EML Trees Are Universal Approximators
Joe Germany, Elie Abdo, Joseph Bakarji
The recently introduced EML (Exp-Minus-Log) function acts as continuous analogue of NAND gates, providing a compositional building block capable of representing elementary function…
Long time dynamics of the Nernst-Planck-Darcy System on
Elie Abdo, Joe Germany, Mohammad Khalil Hamdan +1
We study ionic electrodiffusion modeled by the Nernst--Planck equations describing the evolution of ionic species in a three-dimensional incompressible fluid flowing through a…
Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains
Elie Abdo, Lihui Chai, Ruimeng Hu +1
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Lapl…