Nathan Kirk
Researcher in Computational Mathematics and Statistics
Illinois Institute of Technology, Chicago, USA
My name is Nathan Kirk and I'm a Senior Research Associate at the Department of Applied Mathematics at the Illinois Institute of Technology, Chicago, USA. Before that, I was a researcher in the Department of Statistics and Actuarial Sciences at University of Waterloo, Canada after I finished a PhD in Mathematics at Queen's University Belfast, Northern Ireland supervised by Dr. Florian Pausinger.
My main research interest for the past number of years remains quasi-Monte Carlo sampling schemes and applications. Specifically, I am interested in constructing sampling schemes in the unit hypercube which possess the most uniform distribution, and use these point sets and sequences to replace classical purely random Monte Carlo methods in various simulations and applications as an alternative to variance reduction techniques. Additionally, I am increasingly involved with my collaborators on the intersection between machine learning and quasi-Monte Carlo methods.
Highlighted Work: Message-Passing Monte Carlo (MPMC)
Published in PNAS (Sept 2024)
This article introduces "Message-Passing Monte Carlo (MPMC)", the first machine learning approach for generating low-discrepancy point sets which are essential for efficiently filling space in a uniform manner, and thus play a central role in many problems in science and engineering. To accomplish this, MPMC utilizes tools from Geometric Deep Learning, specifically by employing Graph Neural Networks.
Important Links
(LEFT) Input, random training data.
(RIGHT) Output, generated (learned) low-discrepancy point set
Recent news
September 2024: Our article "Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networks" is accepted in Proceedings of the National Academy of Sciences of the United States of America (PNAS).
August 2024: Together with colleagues Christiane Lemieux and Ben Feng, we organize the primary quasi-Monte Carlo methods conference, MCQMC 2024, at the University of Waterloo. Over 150 participants and talks are expected with 9 plenaries and 2 tutorials.
August 2024: Begin new role as Senior Research Associate in the Department of Applied Mathematics at Illinois Institute of Technology in Chicago, USA, mentored by Prof. Fred Hickernell.
June 2024: "Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networks" is accepted for presentation at the AI4Science Workshop at the International Conference on Machine Learning (ICML) 2024.
June 2024: "An improved Halton sequence for implementation in quasi-Monte Carlo methods" accepted for presentation and publication in Proceedings of the 2024 Winter Simulation Conference.
December 2023: "Partitions for stratified sampling" accepted to Monte Carlo Methods and Applications.
September 2023: Begin new role as Postdoctoral Research Fellow at the University of Waterloo, mentored by Prof. Christiane Lemieux.
June 2023: Successfully defend my PhD thesis "Several Problems in Discrepancy Theory" with examiners Prof. Martin Mathieu and Markus Kiderlin at Queen's University Belfast, Northern Ireland.
February 2023: "On the expected L2-discrepancy of jittered sampling" accepted to Uniform Distribution Theory.
September-October 2022: Visiting PhD student at the University of Waterloo with Prof. Christiane Lemieux.
Logo for MCQMC 2024, designed by Nathan Kirk
Flexing the creative muscles, and taking inspiration from previous MCQMC conference logos, this design by Nathan Kirk will appear for the 30 year anniversary of MCQMC in summer 2024.
