3 papers
math.NA2026
Boundary neuron method for solving partial differential equations
Ye Lin, Wentao Liu, Young Ju Lee +1
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow net…
math.NA2025
R-PINN: Recovery-type a-posteriori estimator enhanced adaptive PINN
Rongxin Lu, Jiwei Jia, Young Ju Lee +2
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread appli…
math.NA2024
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…