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math.NA2026
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…
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…