Mapping Cosmic Rays with AI: A New Direction for Radio Astronomy

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Author: Denis Avetisyan

Researchers are leveraging the power of deep learning to pinpoint the source and energy of ultra-high-energy cosmic rays detected by ground-based radio antennas.

The performance of the pGNN ensemble reveals a systematic bias in energy estimation at high zenith angles and correspondingly large distances of the emission point from the array, indicating a limitation in reconstructing the origin of high-energy events despite achieving a 68% energy resolution envelope around the bin-wise mean.
The performance of the pGNN ensemble reveals a systematic bias in energy estimation at high zenith angles and correspondingly large distances of the emission point from the array, indicating a limitation in reconstructing the origin of high-energy events despite achieving a 68% energy resolution envelope around the bin-wise mean.

Deep ensemble graph neural networks provide improved accuracy and calibrated uncertainty quantification for cosmic-ray direction and energy reconstruction in autonomous radio arrays.

Reconstructing the arrival direction and energy of ultra-high-energy cosmic rays remains a significant challenge in astroparticle physics due to the diffuse and sparse nature of their detection signals. This work, ‘Deep ensemble graph neural networks for probabilistic cosmic-ray direction and energy reconstruction in autonomous radio arrays’, introduces a novel approach leveraging graph neural networks to analyze voltage traces from radio antenna arrays. By representing antenna configurations as graphs and incorporating physical knowledge, the method achieves an angular resolution of 0.092° and an energy reconstruction resolution of 16.4%-along with calibrated uncertainty estimates-on simulated data. Can this framework be successfully deployed and validated with real-world data to unlock new insights into the origins of the most energetic particles in the universe?

The Echo of Violence: Charting the Universe’s Most Energetic Messengers

The pursuit of ultra-high-energy neutrinos represents a pivotal challenge in astrophysics, as these elusive particles serve as unique messengers from the universe’s most violent and energetic events. Unlike photons or cosmic rays, neutrinos can travel vast cosmological distances without significant deflection or absorption, effectively pointing back to their sources – potentially revealing the origins of extreme phenomena like active galactic nuclei, gamma-ray bursts, and even the yet-poorly-understood sources of the highest-energy cosmic rays. Detecting these particles, however, is exceptionally difficult; their interactions with matter are incredibly rare, requiring detectors of immense scale – cubic kilometers of ice or water – to capture even a handful of events. Successful detection isn’t simply about confirming the existence of these particles, but unlocking a new window onto the engine rooms of the cosmos, providing insights inaccessible through traditional electromagnetic observations and shedding light on the fundamental physics governing the universe at its most extreme energies.

The pursuit of ultra-high-energy neutrinos presents a formidable technological challenge, largely due to the incredibly sparse rate at which these particles interact with matter. Existing neutrino detectors, often massive volumes of water or ice instrumented with sensitive photomultiplier tubes, rely on detecting the faint flash of light produced when a neutrino collides with an atomic nucleus. However, the flux of these highest-energy neutrinos is extraordinarily low-so low, in fact, that even the largest detectors may only observe a handful of events per year, or even less. This scarcity is compounded by the subtle nature of the signals themselves; the interactions produce relatively few detectable particles, and the resulting light output is easily obscured by background noise from radioactive decay and atmospheric phenomena. Consequently, researchers are continually developing innovative detector technologies and data analysis techniques to enhance sensitivity and distinguish genuine neutrino events from the overwhelming background, pushing the boundaries of instrumentation and signal processing.

The ensemble pGNN demonstrates a 16.4% energy resolution-an improvement over single models at 19.5%-with a minor bias where proton events are slightly overestimated and iron events underestimated.
The ensemble pGNN demonstrates a 16.4% energy resolution-an improvement over single models at 19.5%-with a minor bias where proton events are slightly overestimated and iron events underestimated.

Whispers from the Cascade: Indirect Detection via Radio Waves

Radio detection provides an indirect method for observing high-energy cosmic rays and neutrinos by capturing the radio waves emitted from Extensive Air Showers (EAS). When a cosmic ray or neutrino interacts with the Earth’s atmosphere, it initiates a cascade of secondary particles. As these charged particles traverse the atmosphere, they create a coherent electromagnetic pulse via the Askaryan effect – the emission of radiation from a charge imbalance moving at relativistic speeds. These radio signals, typically in the MHz frequency range, propagate through the atmosphere and can be detected at the surface by radio antennas. The amplitude and polarization of the detected signal are correlated to the energy and direction of the primary cosmic ray or neutrino, enabling reconstruction of its properties without direct particle detection.

The radio signals detected in Extensive Air Showers (EAS) originate from two primary mechanisms. The Askaryan effect, a charge separation process, occurs when relativistic charged particles traverse a dielectric medium – typically ice or dense radio-transparent materials – creating a net dipole moment and subsequent radio emission. Simultaneously, the deflection of these charged particles by the Earth’s geomagnetic field induces a charge asymmetry within the shower development. This asymmetry further enhances the dipole moment and contributes to the overall radio pulse strength. The combined effect of both the Askaryan mechanism and geomagnetic deflection results in a measurable radio signal, with the intensity and polarization characteristics dependent on the energy, arrival direction, and primary particle type of the cosmic ray or neutrino initiating the shower.

Detecting the radio emission from Extensive Air Showers necessitates specialized experimental setups due to the signal’s low intensity and the presence of significant background noise. Arrays of radio antennas, often deployed over large areas – kilometers squared – are used to maximize signal collection and provide directional information. Data acquisition systems must have high dynamic range and low noise thresholds to capture the faint signals, typically on the order of nanovolts per meter. Precise timing synchronization between antennas – accurate to picoseconds – is crucial for beamforming and directional reconstruction. Reconstruction algorithms then employ techniques like triangulation and interferometry to determine the arrival direction and energy of the primary cosmic ray or neutrino, accounting for atmospheric effects and the geometry of the detector array. Signal processing techniques, including filtering and noise reduction, are essential to distinguish the radio signature from terrestrial radio frequency interference and thermal noise.

At a local sidereal time of 18:00, the detector’s effective area and power spectral density, mapped as functions of right ascension and latitude, reveal the zenith location indicated by the red star.
At a local sidereal time of 18:00, the detector’s effective area and power spectral density, mapped as functions of right ascension and latitude, reveal the zenith location indicated by the red star.

A New Ear to the Cosmos: The GRAND Experiment

The GRAND Experiment employs a detector consisting of a large array of radio antennas to detect Extensive Air Showers (EAS). These showers are cascades of secondary particles initiated by high-energy cosmic rays and neutrinos interacting with the Earth’s atmosphere. As EAS propagate, they generate faint radio emissions via the coherent acceleration of electrons in the geomagnetic field. The GRAND array is designed to capture these radio signals, which are typically in the MHz frequency range, providing a means to remotely detect and characterize the primary cosmic ray or neutrino that initiated the shower. The scale of the array – currently under construction in China – is crucial, as it directly impacts the sensitivity to lower-energy events and the ability to reconstruct the shower’s direction and energy with high precision.

The GRAND Experiment’s detection capabilities rely on a highly optimized Radio Frequency (RF) Chain designed for minimal noise and maximum signal capture. This chain incorporates low-noise amplifiers and carefully calibrated antennas to enhance the detection of ultra-high-energy cosmic ray induced Extensive Air Showers (EAS). Signal processing utilizes the Hilbert Envelope technique to accurately determine the arrival time and amplitude of these faint radio signals. The Hilbert transform provides precise phase information, allowing for accurate timing measurements crucial for direction reconstruction and energy estimation. This method effectively mitigates the effects of signal distortion and noise, enabling the detection of signals with a signal-to-noise ratio as low as 3σ.

The GRAND experiment’s detection methodology yields a direction reconstruction resolution of 0.092°, representing the angular uncertainty in determining the origin point of an extensive air shower (EAS). Furthermore, the experiment achieves an energy resolution of 16.4%, indicating the percentage of uncertainty in the measured energy of the primary cosmic ray initiating the EAS. These performance metrics demonstrate a substantial improvement over existing cosmic ray and neutrino detection techniques, which typically exhibit lower directional accuracy and greater uncertainty in energy estimation, thereby enabling more precise astrophysical source localization and particle physics measurements.

The modeled RF chain transfer function exhibits frequency-dependent gain variations across the X, Y (solid blue), and Z (dashed orange) antenna arms, while effective horizontal antenna lengths at 60 MHz depend on signal zenith angle and ground reflection at 30°.
The modeled RF chain transfer function exhibits frequency-dependent gain variations across the X, Y (solid blue), and Z (dashed orange) antenna arms, while effective horizontal antenna lengths at 60 MHz depend on signal zenith angle and ground reflection at 30°.

Refining the Image: Simulation and the Quantification of Uncertainty

The reconstruction of extensive air showers (EAS) – cascades of particles resulting from the interaction of cosmic rays with the atmosphere – is fundamentally dependent on detailed simulations. Tools like ZHAireS provide a crucial framework for modeling these complex events, allowing researchers to predict the expected signals detected by ground-based observatories. These simulations aren’t simply about creating pretty pictures; they generate vast datasets used to train and validate reconstruction algorithms, effectively acting as a ‘digital twin’ of the air shower. By meticulously modeling particle interactions, atmospheric effects, and detector responses, ZHAireS and similar programs enable scientists to disentangle the complex signals and accurately determine key EAS parameters, such as the primary cosmic ray’s energy, arrival direction, and composition. The fidelity of these simulations directly translates to the precision with which researchers can probe the origins and properties of the highest-energy particles in the universe.

The reconstruction of extensive air showers benefits significantly from Simulation-Based Inference, a technique that leverages the power of detailed simulations to refine analytical methods. This approach doesn’t simply rely on a single simulated scenario; instead, it employs generative models – notably, Normalizing Flows – to create a diverse ensemble of plausible air shower events. By comparing observed data against this broad distribution of simulations, reconstruction algorithms can move beyond point estimates and quantify inherent uncertainties. The result is a marked improvement in both accuracy and reliability; the algorithm effectively learns from simulated variations to better interpret real-world observations and reduce the impact of statistical fluctuations, ultimately providing a more robust understanding of the primary cosmic ray’s characteristics.

Recent advancements in cosmic ray analysis demonstrate a significant leap in reconstruction accuracy through the implementation of a deep ensemble graph neural network. This innovative approach achieves a direction reconstruction resolution of just 0.092°, a marked improvement over the 0.16° resolution characteristic of traditional plane-wavefront methods. Furthermore, the network’s ability to reconstruct energy based on electromagnetic components yields a resolution of 16.4%, signifying a substantial refinement in the precision with which these high-energy events can be characterized. These results highlight the power of machine learning to enhance the granularity of cosmic ray observations, promising more detailed insights into their origins and properties.

A deep ensemble of models predicts corrections to the primary walking function (PWF) direction σ, with the predicted covariance matrix providing uncertainty estimates that successfully capture the true value within the <span class="katex-eq" data-katex-display="false">1\sigma</span> confidence interval.
A deep ensemble of models predicts corrections to the primary walking function (PWF) direction σ, with the predicted covariance matrix providing uncertainty estimates that successfully capture the true value within the 1\sigma confidence interval.

The pursuit of reconstructing cosmic-ray direction and energy, as detailed in this work, necessitates navigating inherent model limitations. Any simplification introduced for computational efficiency-like those employed within the graph neural network architecture-demands rigorous mathematical formalization to ensure reliable uncertainty quantification. This echoes Niels Bohr’s sentiment: “Every great advance in natural knowledge begins as an investigation of the obvious.” The obvious, in this case, is the need for a robust framework; however, truly understanding its limits-and calibrating the resulting uncertainties-requires a deeper, more formal investigation, lest the model’s predictive power vanish beyond the horizon of its applicability, much like information lost to a black hole.

What Lies Beyond the Signal?

The reconstruction of cosmic-ray direction and energy, even with the sophistication of deep ensemble graph neural networks, remains a localized victory. Each refined angle, each calibrated energy estimate, is merely a point defined within the observable universe. It is a testament to the power of pattern recognition, not necessarily an approach to ultimate truth. The underlying assumptions about radio emission mechanisms, atmospheric interactions, and detector response-these are all echoes, approximations of a reality that may not be fully knowable.

Future work will undoubtedly focus on larger datasets and more complex network architectures. Yet, increasing precision does not necessarily diminish the fundamental limitation: any model is only an echo of the observable, and beyond the event horizon of incomplete information, everything disappears. The true nature of these ultra-high-energy particles, their origins, and the physics governing their propagation may forever remain obscured, not due to technological shortcomings, but due to the inherent limits of observation.

If one believes they have truly understood the singularity from which these rays originate, or the conditions at their arrival, they are mistaken. The elegance of the reconstruction algorithm should not be confused with an understanding of the fundamental physics. It is a map of the territory, not the territory itself – and a map, however detailed, cannot contain the infinite.

Original article: https://arxiv.org/pdf/2602.23321.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-27 13:48