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Using Geometric Deep Learning for the Detection of the Diffuse Supernova Neutrino Background in Water-Cherenkov Detectors

This paper introduces a Geometric Deep Learning framework utilizing Graph Neural Networks to enhance the detection and reconstruction of the Diffuse Supernova Neutrino Background in water-Cherenkov detectors by accurately recovering positron energy and classifying neutron capture signals with performance comparable to state-of-the-art methods.

Original authors: Matthieu Melennec, Andrew D. Santos, Thomas Mueller, Frédéric Magniette

Published 2026-10-09

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CC BY 4.0

Original authors: Matthieu Melennec, Andrew D. Santos, Thomas Mueller, Frédéric Magniette

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the universe, a faint, constant hum of ghostly particles drifts through space, carrying the history of every massive star that has ever died in a violent explosion. These particles are neutrinos, and the stream of them created by all the core-collapse supernovae in the cosmos is known as the Diffuse Supernova Neutrino Background. Scientists are eager to catch this signal because it offers a unique way to understand how stars die and to test the fundamental properties of these elusive particles. However, finding this background is incredibly difficult. The signal is weak and arrives at low energies, meaning it is easily drowned out by a sea of noise from natural sources like radioactive decay in the Earth's crust and cosmic rays hitting the atmosphere. To see this faint cosmic whisper, researchers must build detectors large enough to catch a few of these particles and develop methods sharp enough to distinguish them from the overwhelming background static.

One of the most promising places to look for this signal is in massive tanks of ultra-pure water, such as the future Hyper-Kamiokande detector in Japan. When a neutrino from the background interacts with a proton in the water, it triggers a specific two-step reaction. First, it creates a positron, a particle of light matter, which flashes briefly as it moves through the water. A fraction of a millisecond later, a neutron produced in the same reaction is captured by an atomic nucleus, releasing a second, much fainter flash of light. This distinct pair of signals is the fingerprint scientists are looking for. The challenge lies in the fact that the second flash is tiny, often consisting of only a handful of light sensors firing, while the tank is constantly buzzing with random electronic noise. Traditional methods of analyzing these signals rely on fitting mathematical curves to the data, but the complex, cylindrical shape of the detector and the sparse, scattered nature of the light hits make these standard approaches difficult to optimize.

In a recent study, researchers proposed a new way to tackle this problem using a type of artificial intelligence called a Graph Neural Network. Instead of treating the detector as a flat grid or a standard image, they treated the data as a network of connected points. Imagine the light sensors in the water tank as dots on a map, where the dots are connected by lines if they are close to each other in both space and time. This structure allows the computer to see the relationships between the hits naturally, without forcing the data into a shape that doesn't fit the detector's geometry. The team built a computer model that learns to navigate this web of connections to perform two critical tasks: first, to calculate the energy of the initial flash with high precision, and second, to decide whether a faint, delayed flash is a real neutron capture or just random noise.

To test their idea, the researchers simulated the environment of the Hyper-Kamiokande detector using powerful computer programs that mimic how light travels through water and how the sensors respond. They generated millions of fake events, including the desired neutrino signals and the various types of background noise the detector would face in reality. For the first task, the model was trained to look at the pattern of light hits from the initial positron flash and predict its energy. The results were impressive; the model achieved a level of accuracy comparable to the best existing methods used in current detectors, despite the fact that the new detector is larger and has different sensor arrangements. The researchers noted that the model performed particularly well at higher energies, where the light patterns are clearer, and suggested that the model's ability to learn directly from the data without heavy reliance on pre-set physical formulas might explain its success in the lower energy ranges where signals are harder to distinguish.

The second task was even more difficult: identifying the tiny, delayed flash from the neutron capture. In the simulation, this signal appeared as just a few light hits hidden within a massive cloud of random noise over a period of half a millisecond. The researchers first developed a method to clean up this noise by adjusting the timing of the hits based on how long it would take light to travel from the center of the event to each sensor. This process compressed the true signal into a tight cluster while spreading the random noise out, making it easier to spot. They then fed these cleaned-up clusters into their graph-based model. The model learned to look at the connections between the few remaining hits and decide if they formed a real neutron signal. The system proved highly effective, correctly identifying nearly 94% of the true neutron signals while rejecting more than 97% of the background noise. This high level of purity is crucial, as the goal is to find a very rare signal without being misled by false alarms.

The study concludes that this approach, which uses the natural geometry of the data rather than forcing it into a rigid structure, offers a powerful new tool for future neutrino research. The researchers emphasize that their work is a simulation, not a final result from a real detector, but it serves as a strong baseline for what is possible. They suggest that these intelligent networks should not replace existing physics-based methods entirely but rather work alongside them, perhaps helping to validate potential signal locations or refine energy estimates. By combining the pattern-recognition power of modern machine learning with the physical realities of water-based detectors, scientists may soon be able to listen more clearly to the faint, ancient hum of the universe's dying stars.

Technical Summary: Geometric Deep Learning for DSNB Detection in Water-Cherenkov Detectors

Problem Statement
The detection of the Diffuse Supernova Neutrino Background (DSNB) is critical for understanding Core-Collapse Supernovae (CCSNe) and fundamental neutrino properties. However, the DSNB flux is low-energy and competes with significant backgrounds, including reactor neutrinos, cosmic muon spallation, and atmospheric neutrinos. The primary detection channel in water-Cherenkov detectors, such as the future Hyper-Kamiokande (HK), is the Inverse Beta Decay (IBD) interaction. This process produces a two-signal signature: a prompt positron signal (3–30 MeV) and a delayed neutron capture signal (2.2 MeV photon).

Current reconstruction methods rely on fitting signal distributions to regress vertex, timing, and direction, and on extracting specific variables for neutron tagging. These approaches face challenges due to the non-Euclidean geometry of cylindrical detectors (requiring artificial flattening), the sparse nature of low-energy signals (leading to inefficient convolution on empty regions), and irregular photomultiplier tube (PMT) layouts. Furthermore, the strict computational constraints of IBD detection demand algorithms that are both highly efficient and performant to minimize background contamination.

Methodology
The authors propose a Geometric Deep Learning framework based on Graph Neural Networks (GNNs) to address these challenges. The approach treats detector hits as nodes in a graph, utilizing the k-Nearest Neighbors (k-NN) algorithm to construct edges based on space-time proximity (using Euclidean embedding of coordinates $(ct, x, y, z)$).

The pipeline consists of two distinct tasks:

Prompt Positron Energy Regression:
- Pre-processing: Raw data containing $\sim 10^4$ hits is filtered to isolate the prompt signal. An asymmetric Gaussian fit to the hit timing distribution identifies a critical time window ( $\mu - 4\sigma_L$ to $\mu + 3\sigma_R$ ), reducing the graph to $\sim 200$ nodes.
- Graph Construction: Nodes are represented in cylindrical coordinates $(r, \cos\theta, \sin\theta, z)$ to respect detector geometry and avoid angular discontinuities. Features include position, time relative to the peak, and charge.
- Architecture: The model employs message-passing convolution layers where node features are updated by aggregating messages from neighbors. The aggregation uses a mean operator for regression. A Treclus algorithm is used for graph pooling, which clusters nodes based on edge thresholds to coarsen the graph while maintaining linear complexity. A final readout layer uses a feature-wise sum to preserve cluster size information before passing the graph-wide representation to a Multi-Layer Perceptron (MLP) for energy output.
Delayed Neutron Capture Tagging:
- Pre-processing: To isolate the faint 2.2 MeV signal from dark noise, the authors apply a Time-of-Flight (TOF) correction based on the regressed prompt vertex. This concentrates true neutron hits into a narrow 10 ns window while spreading background noise.
- Candidate Selection: A sliding 10 ns window identifies candidate clusters with a minimum hit count ( $N^*_{10} = 7$ ) to ensure a sufficient signal-to-noise ratio.
- Architecture: Similar to the regression task, a GNN is constructed with $k=4$ neighbors. However, due to the small graph diameter ( $\sim 2.5$ ) of these candidate clusters, pooling layers are omitted to avoid unnecessary coarsening. The model uses a max aggregator for convolution and readout, followed by a binary classification MLP trained with Categorical Cross-Entropy Loss.

Key Contributions

GNN Adaptation: The work demonstrates the adaptation of a common geometric deep-learning framework to two complementary IBD tasks: energy regression and neutron tagging, specifically tailored for the irregular, sparse data of water-Cherenkov detectors.
Signal Pre-processing: The introduction of TOF-corrected time spaces and asymmetric Gaussian timing filters to effectively isolate low-energy signals from dark noise without relying on complex triggering mechanisms.
Architecture Design: The implementation of the Treclus pooling algorithm to handle graph coarsening with linear complexity and the specific choice of aggregation operators (sum for regression to preserve density, max for classification).

Results

Energy Regression: The model achieves an energy resolution comparable to the state-of-the-art effective number of hits ( $N_{eff}$ ) method used in Super-Kamiokande and extended to Hyper-Kamiokande. Notably, performance improves for positron energies above 20 MeV, where signal definitions are clearer. The authors note the resolution curve does not strictly follow the standard $\sigma(E)/E$ parameterization, potentially due to the data-driven nature of the training.
Neutron Tagging: The classifier achieves a 97.47% background rejection rate while identifying 93.98% of selected neutron candidates. The Receiver Operating Characteristic (ROC) curve indicates a strong ability to distinguish true neutron signals from dark noise, with an asymmetric error rate favorable for background-dominated searches.

Significance and Claims
The paper claims that GNNs provide a promising framework for low-energy event reconstruction in water-Cherenkov detectors, offering performance comparable to state-of-the-art methods while naturally handling non-Euclidean geometries and sparse data.

The authors modestly position their work as a baseline for applying modern machine learning to neutron tagging in next-generation detectors. They emphasize that GNN-based reconstruction is best integrated with established physics-driven methods rather than used as a fully standalone approach. For instance, they suggest using GNNs to validate vertices for grid-search algorithms (like BONSAI) or to refine energy estimates based on effective hit counts. The study concludes that while the current models are effective, further integration of detector specifications (such as fiducial volume filtering) and physics-informed constraints could enhance performance.

Technical Summary: Geometric Deep Learning for DSNB Detection in Water-Cherenkov Detectors

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