Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

This book is focused on a powerful numerical methodology for solving PDEs to high
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …

Mesh motion using radial basis functions has been demonstrated previously by the authors
to produce high quality meshes suitable for use within unsteady and aeroelastic CFD codes …

Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

Time-dependent advection–diffusion–reaction and diffusion–reaction equations are used as
models in biology, chemistry, physics, and engineering. As representative examples, we …

The acquisition of labels for supervised learning can be expensive. To improve the sample
efficiency of neural network regression, we study active learning methods that adaptively …

Positive definite kernels play an increasingly prominent role in many applications such as
scattered data fitting, numerical solution of PDEs, computer experiments, machine learning …

Previous work by the authors has developed an efficient method for using radial basis
functions (RBFs) to achieve high quality mesh deformation for large meshes. For volume …