Novel directionality algorithm from student-led team selected as featured journal article

Many areas of science and engineering face the same challenge: how to infer a preferred direction when the information is spread across many measurements rather than appearing as a single clear feature. This arises in particle physics and astronomy, as well as in imaging and machine learning, whenever data take the form of a two-dimensional grid, or histogram.

A student-led team from the University of Hawai‘i and LLNL has produced a new algorithm for extracting direction from noisy, two-dimensional data. The team’s work, originally motivated by a neutrino detector design problem and performed as part of the Consortium for Monitoring, Technology, and Verification, was recently selected as a “featured article” in AIP Advances and an AIP “Scilight.”

The team’s key innovation is the use of a tool called the continuous Frobenius norm of the difference (CFND) to compare smooth, continuous data in two dimensions. CFND is an extension of the Frobenius norm, a standard way to measure the difference between two matrices. In their approach, each 2D dataset is represented as a histogram that can be mapped to a continuous function. A measured dataset of unknown orientation is compared to a reference dataset with known orientation by systematically “rotating” one through all possible angles and computing the CFND at each angle, which acts like a mismatch score. The angle at which the CFND is smallest corresponds to the most likely direction in the measured data.

Rather than relying solely on numerical trial and error, the research team, led by University of Hawai‘i undergraduate Jeffrey G. Yepez, derives a theoretical, continuous version of this comparison tool. By modeling the data as smooth, bell-shaped (Gaussian) patterns, the researchers obtain a precise mathematical expression for the CFND: when the directional bias is small compared to the width of the data distribution, the CFND behaves like the absolute value of a sine function of the angle. The minimum of this curve directly identifies the inferred direction.

This approach offers several positive features and potential advantages over other methods. It compares entire patterns, not just a single summary statistic such as a central peak. By averaging information across all angles, it naturally reduces the impact of random noise and works well even when the data are sparse or low resolution. The method also provides mathematical formulas that explain why it works and how it will behave under different conditions, which is valuable for designing experiments and detectors.

“Our original goal was to refine direction reconstruction in segmented inverse beta-decay detectors, but along the way we discovered that the underlying optimization had a much broader and more fundamental structure,” said NACS physicist Viacheslav Li. “It is especially rewarding to see this recognized as featured article, given how much of the work was driven by students.”

Yepez led much of the analysis and algorithm development, under the mentorship of Li and University of Hawai‘i collaborators. Yepez notes, “One of the most enjoyable aspects of this project was turning a very intuitive question—does this distribution have a directional bias?—into a rigorous and broadly applicable mathematical method.”

While the original application is in neutrino detection, the CFND-based method has potential uses wherever researchers need to recover direction from noisy 2D data, including astronomy, image analysis, and machine learning. Further, the framework, developed for two dimensions, could in principle be extended to three. This publication complements ongoing LLNL efforts in advanced neutrino detection, detector algorithms, and rare-event searches, and illustrates how revisiting a familiar mathematical tool in a new context can yield a powerful solution to a long-standing problem.

[J.G. Yepez, J.D. Seligman, M.A.A. Dornfest, B.C. Crow, J.G. Learned, and V.A. Li, Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm, AIP Advances (2026), doi: 10.1063/5.0315079.]

–Physical and Life Sciences Communications Team