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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…
math.NA2022★ 1 cited
Higher-Order error estimates for physics-informed neural networks approximating the primitive equations
Ruimeng Hu, Quyuan Lin, Alan Raydan +1
Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generall…