4 citations · 4 across the 5 of their papers we have counts for
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Randomized Radial Basis Function Neural Network for Solving Multiscale Elliptic Equations
Yuhang Wu, Ziyuan Liu, Wenjun Sun +1
To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approac…
SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions
Ziyuan Liu, Yuhang Wu, Daniel Zhengyu Huang +3
Neural operators have been validated as promising deep surrogate models for solving partial differential equations (PDEs). Despite the critical role of boundary conditions in PDEs,…
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…
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…
Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schrödinger equation in one and two dimensions
Ziyuan Liu, Hong Zhang, Xu Qian +1
We present and analyze a series of conservative diagonally implicit Runge--Kutta schemes for the nonlinear Schrödiner equation. With the application of the newly developed invarian…