2 papers
math.NA2026
Sparse RBF Networks for PDEs and nonlocal equations: function space theory, operator calculus, and training algorithms
Zihan Shao, Konstantin Pieper, Xiaochuan Tian
This work presents a systematic analysis and extension of the sparse radial basis function network (SparseRBFnet) previously introduced for solving nonlinear partial differential e…
math.NA2025
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks
Zihan Shao, Konstantin Pieper, Xiaochuan Tian
We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameteriz…