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20232026
most citedOn the Long-time Dynamics and Ergodicity of the Stochastic Nernst-Planck-Navier-Stokes System

1 citations · 2 across the 13 of their papers we have counts for

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math.NA2024

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),…

math.NA2024★ 1 cited

A PDE Perspective on Approximating Nonlocal Periodic Operators with Applications on Neural Networks for Critical SQG Equations

Elie Abdo, Ruimeng Hu, Quyuan Lin

Nonlocal periodic operators in partial differential equations (PDEs) pose challenges in constructing neural network solutions, which typically lack periodic boundary conditions. In…