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math.NA2024★ 3 cited
Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators
Anran Jiao, Qile Yan, Jhn Harlim +1
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown…
math.NA2024
Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
Rongji Li, Qile Yan, Shixiao W. Jiang
In this paper, we extend the Generalized Moving Least-Squares (GMLS) method in two different ways to solve the vector-valued PDEs on unknown smooth 2D manifolds without boundaries…