5 papers
Constrained Optimal Polynomials for Quantum Linear System Solvers
Matthias Deiml, Daniel Peterseim
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation a…
Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients
Fabian Kröpfl, Daniel Peterseim, Elisabeth Ullmann
This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical h…
Quantum Sampling and Moment Estimation for Transformed Gaussian Random Fields
Matthias Deiml, Daniel Peterseim
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on -dimensional domains, based on an enhanced version of the classical moving average…
Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity
Camilla Belponer, José C. Garay, Peter Munch +1
We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a he…
Nonlinear quantum computation by amplified encodings
Matthias Deiml, Daniel Peterseim
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evalu…