5 papers
Near-Optimal Learning of Gaussian Sobolev Operators
Ben Adcock, Michael Griebel, Gregor Maier
A key question in operator learning is how to design surrogate operators with provable approximation guarantees in reasonable computational time. Whereas smooth operators can be ap…
Sparse Configuration Interaction for the Electronic Schrödinger Equation Revisited: Complete Basis Set Limit Complexity and Quantum-Encoding Impact
Michael Griebel, Jan Hamaekers
In this article we revisit regularity results for eigenfunctions in the discrete spectrum of the electronic Schrödinger equation and study their consequences for approximation com…
Kernel interpolation on generalized sparse grids
Michael Griebel, Helmut Harbrecht, Michael Multerer
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and…
The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
Ben Adcock, Michael Griebel, Gregor Maier
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Appr…
Efficient solution of ill-posed integral equations through averaging
Michael Griebel, Tim Jahn
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ…