5 papers · 1 filter
Greedy Algorithm for Neural Networks for Indefinite Elliptic Problems
Qingguo Hong, Jiwei Jia, Young Ju Lee +1
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of th…
fOGA: An Orthogonal Greedy Algorithm for Fractional Laplacian Problems
Ruitong Shan, Young Ju Lee, Jiwei Jia
In this paper, we propose a numerical method for fractional Laplace equations that combines finite difference discretization with shallow neural network approximation. The fraction…
The pressure-robust weak Galerkin finite element method for Stokes-Darcy problem
Jiwei Jia, Lin Yang, Qilong Zhai
In this paper, we propose a pressure-robust weak Galerkin (WG) finite element scheme to solve the Stokes-Darcy problem. To construct the pressure-robust numerical scheme, we use th…
Green Multigrid Network
Ye Lin, Young Ju Lee, Jiwei Jia
GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential e…
An Unconstrained Formulation of Some Constrained Partial Differential Equations and its Application to Finite Neuron Methods
Jiwei Jia, Young Ju Lee, Ruitong Shan
In this paper, we present a new framework how a PDE with constraints can be formulated into a sequence of PDEs with no constraints, whose solutions are convergent to the solution o…