5 citations · 7 across the 6 of their papers we have counts for
6 papers
Neural Low-Discrepancy Sequences
Michael Etienne Van Huffel, Nathan Kirk, Makram Chahine +2
Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including…
On the optimization of discrepancy measures
François Clément, Nathan Kirk, Art B. Owen +1
Numerical optimizations can find point sets with lower discrepancies than prior methods based on algebra, and discrepancies are computationally attractive for this. The …
Low Stein Discrepancy via Message-Passing Monte Carlo
Nathan Kirk, T. Konstantin Rusch, Jakob Zech +1
Message-Passing Monte Carlo (MPMC) was recently introduced as a novel low-discrepancy sampling approach leveraging tools from geometric deep learning. While originally designed for…
An improved Halton sequence for implementation in quasi-Monte Carlo methods
Nathan Kirk, Christiane Lemieux
Despite possessing the low-discrepancy property, the classical d dimensional Halton sequence is known to exhibit poorly distributed projections when d becomes even moderately large…
Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks
T. Konstantin Rusch, Nathan Kirk, Michael M. Bronstein +2
Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficient…
Golden Ratio Nets and Sequences
Nathan Kirk, Christiane Lemieux, Jaspar Wiart
In this paper we introduce and study nets and sequences constructed in an irrational base, focusing on the case of a base given by the golden ratio . We provide a complete frame…