6 papers
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…
Error estimates of physics-informed neural networks for approximating Boltzmann equation
Elie Abdo, Lihui Chai, Ruimeng Hu +1
Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023),…
Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation
Elie Abdo, Quyuan Lin, Changhui Tan
The primitive equations (PE) are a fundamental model in geophysical fluid dynamics. While the viscous PE are globally well-posed, their inviscid counterparts are known to be ill-po…
Electroconvection in a Magnetic Field
Elie Abdo, Peter Constantin, Mihaela Ignatova +1
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak soluti…