This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

In the past two decades, meshfree methods have emerged into a new class of computational
methods with considerable success. In addition, a significant amount of progress has been …

Radial basis function methods are modern ways to approximate multivariate functions,
especially in the absence of grid data. They have been known, tested and analysed for …

RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very
powerful and flexible numerical approach for solving a wide range of PDEs. We find in the …

The goal of learning theory is to approximate a function from sample values. To attain this
goal learning theory draws on a variety of diverse subjects, specifically statistics …

Data-driven models are subject to model errors due to limited and noisy training data. Key to
the application of such models in safety-critical domains is the quantification of their model …

For interpolation of scattered multivariate data by radial basis functions, an “uncertainty
relation” between the attainable error and the condition of the interpolation matrices is …

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 …

The dynamic positioning system (DPS) is a complex mechatronic system consisting of
multiple sub-disciplines. For such highly coupled sub-disciplines and sub-systems within the …

We address the problem that occurs when inferences about counterfactuals—
predictions,“what-if” questions, and causal effects—are attempted far from the available …