2 papers
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…
math.NA2022
An Operator Learning Approach via Function-valued Reproducing Kernel Hilbert Space for Differential Equations
Kaijun Bao, Xu Qian, Ziyuan Liu +1
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this en…