4 papers
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…
Uncertainty Quantification for Quantum Computing
Ryan Bennink, Olena Burkovska, Konstantin Pieper +2
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathe…
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…
Nonuniform random feature models using derivative information
Konstantin Pieper, Zezhong Zhang, Guannan Zhang
We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. These parameter distributio…