Render unto Numerics : Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions

  title={Render unto Numerics : Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions},
  author={Ziyuan Liu and Haifeng Wang and Kaijun Bao and Xu Qian and Hong Zhang and Songhe Song},
By learning the map between function spaces using carefully designed deep neural networks, the operator learning become a focused field in recent several years, and have shown considerable efficiency over traditional numerical methods on solving complicated problems such as differential equations, but the method is still disturbed with the concern of its accuracy and reliability. In this paper, combined with the structures and technologies of a popular numerical method, i.e. the spectral method, a… 

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