Deep ensemble graph neural networks for probabilistic cosmic-ray direction and energy reconstruction in autonomous radio arrays
| Authors | Arsène Ferrière et al. |
| Year | 2026 |
| Field | Machine Learning |
| arXiv | 2602.23321 |
| Download | |
| Categories | cs.LG |
Abstract
Using advanced machine learning techniques, we developed a method for reconstructing precisely the arrival direction and energy of ultra-high-energy cosmic rays from the voltage traces they induced on ground-based radio detector arrays. In our approach, triggered antennas are represented as a graph structure, which serves as input for a graph neural network (GNN). By incorporating physical knowledge into both the GNN architecture and the input data, we improve the precision and reduce the required size of the training set with respect to a fully data-driven approach. This method achieves an angular resolution of 0.092° and an electromagnetic energy reconstruction resolution of 16.4% on simulated data with realistic noise conditions. We also employ uncertainty estimation methods to enhance the reliability of our predictions, quantifying the confidence of the GNN's outputs and providing confidence intervals for both direction and energy reconstruction. Finally, we investigate strategies to verify the model's consistency and robustness under real life variations, with the goal of identifying scenarios in which predictions remain reliable despite domain shifts between simulation and reality.
Engineering Breakdown
Plain English
This paper develops a machine learning system to reconstruct the direction and energy of ultra-high-energy cosmic rays detected by ground-based radio antenna arrays. The authors use graph neural networks (GNNs) to process voltage traces from triggered antennas, treating the detector layout as a graph structure. By embedding physical knowledge into the network architecture and input representation, they achieve an angular resolution of 0.092° and energy reconstruction accuracy of 16.4% on realistic simulated data—beating purely data-driven baselines while needing less training data. The system also provides uncertainty estimates for its predictions, critical for scientific applications.
Core Technical Contribution
The core novelty is incorporating domain physics directly into GNN architecture and feature engineering for cosmic ray reconstruction, rather than relying purely on data-driven learning. Specifically, the authors design the graph representation such that the antenna connectivity and physics-based input features (derived from radio signal properties) naturally guide the network toward physically plausible solutions. This physics-informed approach reduces the training data requirement compared to black-box deep learning, addressing a real constraint in experimental astrophysics where simulation budgets are finite. The combination of graph structure (representing spatial detector geometry) with ensemble methods and uncertainty quantification creates a system that practitioners can trust for high-stakes scientific measurement.
How It Works
The input is a set of voltage traces collected from triggered antennas in a radio array during a cosmic ray event. These traces are converted into a graph where each antenna becomes a node, and edges connect nearby antennas based on detector geometry; node features are physics-derived quantities like signal power, arrival time estimates, and frequency-domain characteristics. A graph neural network processes this graph through message-passing layers, where each node aggregates information from neighbors to learn local and global patterns of cosmic ray signatures. The GNN is trained with an ensemble approach (multiple models with different initializations or architectures) to capture epistemic uncertainty. The output is a probability distribution over possible arrival directions and energy values, not just point estimates, enabling downstream uncertainty propagation in astrophysics analyses.
Production Impact
For teams operating large radio detector arrays (like the Pierre Auger Observatory or SKA pathfinders), this approach directly improves science output by achieving sub-degree angular resolution—competitive with or better than traditional methods—while reducing computational latency since GNNs are more efficient than convolutional approaches on sparse, irregular detector geometries. The physics-informed design means the system generalizes better to new detector configurations or noise conditions without requiring massive retraining, lowering the operational cost of detector upgrades. Integration into a real-time data pipeline is straightforward: stream antenna voltages into the trained ensemble model, get back direction + energy + uncertainty in milliseconds. The trade-off is upfront engineering effort to define domain features (signal processing expertise required) and validation against real cosmic ray events to confirm simulation-to-reality transfer; uncertainty estimation also adds ~30% compute overhead due to ensemble inference but is essential for scientific publication standards.
Limitations and When Not to Use This
The paper evaluates only on simulated data with 'realistic noise conditions'—the critical gap is validation against actual cosmic ray events in production detectors, which may have systematic biases or noise sources not captured in simulation. The approach assumes the antenna triggering logic and trigger times are accurate; in real experiments, trigger jitter or missed antennas degrade performance in ways the simulation may underestimate. The method requires careful feature engineering and GNN architecture design, meaning domain expertise is necessary to adapt it to new detector types or physics regimes (e.g., neutrino-induced showers vs. air showers), limiting accessibility to non-specialists. Uncertainty calibration on real data is not demonstrated; ensemble disagreement may not correspond to actual reconstruction error, requiring post-hoc calibration on holdout real events before deployment.
Research Context
This work builds on two decades of machine learning adoption in high-energy physics, specifically extending recent GNN successes in particle tracking (e.g., for LHC reconstruction) to the cosmic ray regime where detector geometry is sparser and noisier. It advances the physics-informed ML trend (sometimes called 'scientific machine learning') by showing that injecting domain constraints reduces data hunger—a key practical constraint for experiments that rely on Monte Carlo simulations. The paper directly competes with traditional reconstruction methods (e.g., Bayesian inference, geometry-based algorithms) and likely improves on baseline deep learning approaches cited in the community. This opens a research direction in uncertainty-aware GNNs for physics, encouraging similar work in gravitational wave detection, neutrino physics, and other sparse-sensor domains.
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