1 citations · 1 across the 2 of their papers we have counts for
4 papers
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…
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…
Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis
Xiaochuan Tian, Yixuan Wu, Yanzhi Zhang
The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric function…
A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems
Yimeng Zhang, Alexander Cloninger, Bo Li +1
We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for system…