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math.NA2022
Cell-average based neural network method for high dimensional parabolic differential equations
Hong Zhang, Hongying Huang, Jue Yan
In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral…
math.NA2022
Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions
Ziyuan Liu, Haifeng Wang, Hong Zhang +3
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency th…