Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Nonperiodic Boundary Conditions: Render unto numerics: orthogonal polynomial neural operator for PDEs with nonperiodic boundary conditions

Authors: Ziyuan Liu, Haifeng Wang, Hong Zhang, Kaijun Bao, Xu Qian, Songhe Song

Source: SIAM Journal on Scientific Computing. 46:C323-C348

Subject Terms: scientific machine learning, deep learning-based PDE solver, Computational methods for problems pertaining to operator theory, Computational learning theory, spectral method, Numerical Analysis (math.NA), neural operator, 01 natural sciences, Algorithms for approximation of functions, AI4science, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2206.12698
https://zbmath.org/7883828
https://doi.org/10.1137/23m1556320