3 citations · 3 across the 4 of their papers we have counts for
4 papers
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
Two families of -rectangle nonconforming finite elements for sixth-order elliptic equations
Xianlin Jin, Shuonan Wu
In this paper, we propose two families of nonconforming finite elements on -rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent propert…
Greedy Training Algorithms for Neural Networks and Applications to PDEs
Jonathan W. Siegel, Qingguo Hong, Xianlin Jin +2
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engi…
A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrödinger equations
Hongling Hu, Xianlin Jin, Dongdong He +2
In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schrödinger equation (SFNSE).The sche…