From Workshop to Publication: PNNL Researchers Advance Hypergraph Science

Researchers at Pacific Northwest National Laboratory (PNNL) are frequently involved in communities and groups that accelerate scientific research and development. One such group is the Mathematics Research Communities Program (MRC) funded by the American Mathematical Society. The MRC program, founded in 2008, features over 1,500 alumni from 48 different areas of focus and offers mentorship, networking, and collaborative opportunities in specialized research areas.

Flashback to 2021

Historically, this program solicited proposals from academics, but this changed in 2021 when the MRC put out a call for proposals related to business, industry, and government (BIG). With the clever acronym of BIG, it's no surprise it caught the attention of multiple staff at PNNL.

MRC was looking for a cohort of individuals with proposals related to BIG math problems who could lead a summer, week-long workshop attended by students, postdocs, and early-career researchers in 2022.

Emilie Purvine, a senior data scientist at PNNL, recalled seeing the offering: "We thought, hey, we're government. We're kind of industry too. And we have cool math problems!" This led the self-assembled team of researchers from multiple Department of Energy laboratories to submit a proposal to lead a workshop, which they were awarded. 

In addition to Purvine, the team included: 

Collectively, the team organized the workshop and corresponding paper, "Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government," which sought to advance data-driven system analysis by developing sophisticated graph and hypergraph models to analyze complex networks across critical domains, such as computer systems, infrastructure, biology, and social networks.

With hypernetwork science as their core focus, the team developed six different groups and six different problems among their selected workshop attendees—with each group being led by an individual from the organizing team.

Current day 

Purvine remarked on the initial outcomes of the workshop, "It isn't possible to finalize an entire paper or project in a span of a week, but you can start the ideas and build collaborative relationships." 

This led some of the teams established during the workshop to continue working on their corresponding paper or project even after it concluded. The continuation of this work was largely team-driven, with opportunities for follow-up and special sessions at the Joint Mathematics Meetings being supported by the American Mathematical Society. 

Broader impacts also included the publication of papers by both Aksoy and Young. While their papers “Scalable Tensor Methods for Nonuniform Hypergraphs” and “HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network” were not a direct result of MRC, the content was informed by the ideas that participants and organizers discussed over the course of the MRC.  

Featured publications

Among the teams that received publication of their papers as a direct result of the MRC were the teams led by Purvine, Joslyn, and Kay.

Purvine’s team: making topological data analysis smarter and faster 

Purvine’s team successfully published “G-Mapper: Learning a Cover in the Mapper Construction” in the SIAM Journal on Mathematics of Data Science. Together, the team developed a new algorithm that automatically fine-tunes the mapper visualization technique, making topological data analysis both more accurate and significantly faster than previous methods.

On the impact of their work, Purvine added, “Setting parameters for the Mapper algorithm has historically been part art. Our work, together with other recent advances, helps to make the parameter tuning more data-driven and less subjective.”

Kay’s team: unveiling hidden structures in hypergraphs 

A breakthrough in understanding complex network structures was demonstrated through an information-theoretic algorithm for hypergraph community detection, which was developed by Kay's team, and presented in their paper "Community detection in hypergraphs via mutual information maximization" published by Scientific Reports. "Information theory provides a framework for finding descriptive, compressed versions of complex objects," Kay explained. 

"With a little bit of imagination (and a lot of work), these descriptions can be used to find meaningful community structure in complex relational networks," such as friendships in social networks or playlists of songs. "Using tools that were meant to improve communication systems," he added, "we are learning more about scientific data systems every day." 

Joslyn’s team: bridging connections and attributes in hypernetworks 

Joslyn's team introduced a novel approach to join the structural information about connections in hypernetworks with the data and attributes which sit on those connections, when projected to pairwise interactions for usability. This resulted in the paper titled, "Understanding high-order network structure using permissible walks on attributed hypergraphs," which has just been published in the Journal of Complex Networks. 

“This MRC proved a unique opportunity not just for PNNL staff, but also in my group a PNNL postdoc and a PNNL student intern, to team with the future academic leaders in our field to advance the state of the art in ways we couldn't have anticipated,” said Joslyn. 

Looking ahead

Programs like the MRC provide more value than just the output created from them in the way of finalized papers or projects. They also offer the opportunity for community and continued collaboration. Purvine, who also once participated in an MRC workshop as an attendee, reflected on the MRC, "It really changed the course of my career. I learned about new areas of math and met some incredible people that are still part of my community."

Kay, who still meets regularly with some of his team shared, “We are investigating new and exciting ways to put the knowledge and camaraderie built by the MRC to good use. The work that we started at the MRC was exciting, but I can't help feeling like the best is yet to come."

For more information about the MRC and its corresponding opportunities for involvement, visit here.