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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
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…
math.NA2024
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…