Reconstruction of Energy of Ultra-High-Energy Cosmic Rays Registered with a Fluorescence Telescope: One Time Frame Might Be Enough

TL;DR

The paper addresses reconstructing the energy of ultra-high-energy cosmic rays detected by a small fluorescence telescope when only a single frame is available, a situation where conventional time-series-based methods fail. It demonstrates that an ensemble of simple convolutional neural networks, combined with a convolutional encoder-decoder for track labeling, can estimate primary energy without full shower geometry in many cases. Results on three EUSO-TA events show two energies are reasonably close to Telescope Array values, while one event remains challenging and motivates training-data augmentation with more diverse shower geometries. The study highlights the promise of neural-network–based energy reconstruction for fluorescence telescopes and outlines directions to improve track-recognition robustness and dataset coverage for broader applicability.

Abstract

We address the challenge of reconstructing the energy of three ultra-high-energy cosmic rays registered with a small fluorescence telescope EUSO-TA that operated in 2015 at the site of the Telescope Array experiment in Utah, USA. Each of these events was recorded within one time frame. Conventional methods of energy reconstruction are not applicable in this case because the events do not have light curves but a single data point. As an alternative, we consider a number of approaches based on artificial neural networks. We demonstrate that a signal recorded by a fluorescence telescope within one time frame might be enough to reconstruct the energy of a primary particle with reasonable accuracy using an ensemble of simple convolutional neural networks. Contrary to the conventional approach, reconstruction of the shower geometry is not needed for this. More than this, preliminary estimates can be obtained even without recognizing the shower track. However, there remain some problems that do not allow us to claim that the suggested method is universal and always works. We discuss difficulties that we faced and possible ways of improving the method.

Figures (10)

• Figure 1: From left to right: snapshots of the EUSO-TA photodetector at the moments of registering UHECRs on 2015-05-13, 2015-10-15, 2015-11-07, and the mask employed to exclude data corresponding to malfunctioning pixels. Zeros in the mask indicate pixels that were ignored.
• Figure 2: An example of energy reconstruction for 1000 events with a CNN trained to predict only energy (one of "Models E"). Left: predictions of the model. Ground truth labels are indicated by circles. Red diamonds show predictions that are within 15% error from the true ones. Blue triangles pointed up and down show predictions overestimated and underestimated by more than 15% respectively. Right: distribution of relative errors over energy of events in the test sample.
• Figure 3: An example of energy reconstruction for 1000 events with a CNN trained to predict energy without any information about EAS tracks. Notation is the same as in Fig. \ref{['ysems']}.
• Figure 4: Distribution of MAPE in predictions of energy for three sets of models: models trained to reconstruct only energy with tracks recognized by the CED (Models E), models trained to reconstruct both energy and the distance from the FT to the shower core with tracks recognized the same way (Models (E, dist)), and models trained to reconstruct energy without any knowledge about EAS tracks (NL-NT E). Vertical lines of three colors indicate mean values of MAPE for the respective sets.
• Figure 5: Recognition of active pixels in the event registered on 2015-05-13. From left to right: the original signal; the flat-fielded signal (with the mask applied); prediction of the CED; activated pixels as predicted with the threshold level 0.5.