2 papers
math.NA2026
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…
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…