4 papers · 1 filter
Anisotropic Kernel-based Multilevel Interpolation of High-Dimensional Functions on Sparse Grids
Rüdiger Kempf
The tensor product multilevel method (TPML) approximates high-dimensional functions from scattered data on general bounded domains by combining Smolyak's sparse grid construction w…
Samplet compression for conditionally positive definite kernels and universal Kriging
Sara Avesani, Rüdiger Kempf, Michael Multerer +1
We present a samplet-based framework for the efficient numerical solution of saddle-point systems arising from conditionally positive definite (CPD) kernel approximation in general…
Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
Rüdiger Kempf
We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator fr…
Nodal Representations for Kernel-Based Multilevel Interpolation
Lorenz Gollwitzer, Rüdiger Kempf, Holger Wendland
We study the kernel-based multilevel method for approximating or learning a multivariate function from scattered data, motivated in part by recent applications in sparse grid metho…