6 papers · 1 filter
A Locally Conservative Enriched Linearized Neural Network Approximation to Elliptic PDEs
Seungil Kim, Gwanghyun Jo, Young Ju Lee
This paper presents a locally conservative Enriched Linearized Neural Network (ENN) method for the Darcy flow model. A linearized shallow ReLU network, whose hidden-layer param…
Orthogonal greedy algorithm for linear operator learning with shallow neural network
Ye Lin, Jiwei Jia, Young Ju Lee +1
Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven effective in training shallow neural networks for fitting functions and solving partial different…
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…
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…
Positivity and Maximum Principle Preserving Discontinuous Galerkin Finite Element Schemes for a Coupled Flow and Transport
Shihua Gong, Young-Ju Lee, Yukun Li +1
We introduce a new concept of the locally conservative flux and investigate its relationship with the compatible discretization pioneered by Dawson, Sun and Wheeler [11]. We then d…