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math.NA2025
Robust and efficient solvers for nonlinear partial differential equations based on random feature method
Longze Tan
The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-…
math.NA2024
High-precision randomized iterative methods for the random feature method
Jingrun Chen, Longze Tan
This paper focuses on solving large-scale, ill-conditioned, and overdetermined sparse least squares problems that arise from numerical partial differential equations (PDEs), mainly…