3 papers
math.NA2026
A Novel Method for Enforcing Exactly Dirichlet, Neumann and Robin Conditions on Curved Domain Boundaries for Physics Informed Machine Learning
Suchuan Dong, Yuchuan Zhang
We present a systematic method for exactly enforcing Dirichlet, Neumann, and Robin type conditions on general quadrilateral domains with arbitrary curved boundaries. Our method is…
math.NA2024
Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks
Yianxia Qian, Yongchao Zhang, Suchuan Dong
We present the hidden-layer concatenated physics informed neural network (HLConcPINN) method, which combines hidden-layer concatenated feed-forward neural networks, a modified bloc…
math.NA2023
An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions
Yiran Wang, Suchuan Dong
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation pro…