Event Reconstruction for Radio-Based In-Ice Neutrino Detectors with Neural Posterior Estimation

TL;DR

This work tackles the challenge of reconstructing ultra-high-energy neutrino properties from in-ice radio signals by applying neural posterior estimation with conditional normalizing flows to produce event-by-event posteriors for energy and direction, plus a topology classifier for flavor. The approach is trained on large NuRadioMC/NuRadioReco simulations for IceCube-Gen2 Radio's shallow and deep components, achieving improved energy and direction resolutions and enabling a goodness-of-fit test to assess compatibility with training data. It demonstrates that joint energy-vertex correlations and polarization information drive uncertainty contours that are often highly non-Gaussian, and shows how antenna choice and systematic uncertainties affect performance. The methodology provides a robust framework to incorporate systematics into posteriors, aiding detector design and calibration while offering practical tools for event selection and background rejection in in-ice radio neutrino astronomy.

Abstract

The detection of ultra-high-energy (UHE) neutrinos in the EeV range is the goal of current and future in-ice radio arrays at the South Pole and in Greenland. Here, we present a deep neural network that can reconstruct the main neutrino properties of interest from the raw waveforms recorded by the radio antennas: the neutrino direction, the energy of the particle shower induced by the neutrino interaction, and the event topology, thereby estimating the neutrino flavor. For the first time, we predict the full posterior PDF for the energy and direction reconstruction via neural posterior estimation utilizing conditional normalizing flows, enabling event-by-event uncertainty prediction. We improve over previous reconstruction algorithms and obtain a median resolution of 0.30 log(E) and 18 square degrees for a 'shallow' detector component and 0.08 log(E) and 28 square degrees for a 'deep' detector component for neutral current (NC) events at a shower energy of 1 EeV. This deep learning approach also allows us to reconstruct the more stochastic $ν_e$ - charged current (CC) events. We quantify the impact of different antenna types and systematic uncertainties on the reconstruction and derive a goodness-of-fit score to test the compatibility of measured neutrino signals with the Monte Carlo simulations used to train the neural network.

Figures (15)

• Figure 1: 'Hybrid' radio station with the antennas relevant for neutrino detection as envisioned for IceCube-Gen2 Radio. The 'shallow' component of the station encompasses four LPDA antennas and one Vpol antenna, while the 'deep' component of the station encompasses 12 Vpol antennas and four Hpol antennas.
• Figure 2: Neural network architecture schematic developed for this reconstruction. Starting from the input data at the top, the data flows through several 1d convolutional layers before being handed to multiple blocks of ResNet layers. After pooling the output from the ResNet Blocks the compressed data is handed to the conditional normalizing flows for the direction and energy prediction, as well as a classifier for the event topology prediction. Two separate models were trained for the 'shallow' and 'deep' detector components but large parts of the network architecture are identical, with differences arising during hyperparameter tuning.
• Figure 3: Overview of the model output for a single event. Top left: Full sky map with the predicted neutrino direction PDF visible as a small dot. Top right: Zoomed-in sky map of the PDF of the predicted neutrino direction. The 68% uncertainty contour of the predicted PDF is shown in orange, and the MC true direction of the event is shown as a black cross. Center-left: Classification results where the model predicts a confidence for the '$\nu_x$ - NC' or '$\nu_e$ - CC' event topology, while '$\nu_x$ - NC' was the MC true event topology. Bottom: Predicted shower energy PDF with the 68% uncertainty region indicated in orange, and the MC true shower energy indicated as a dashed line. This is the marginalized distribution from the 4-dimensional PDF, which also includes the vertex position. The correlations between the shower energy prediction and the vertex position prediction for the same event can be seen in figure \ref{['fig:correlations']}, and the event trace can be seen in figure \ref{['fig:shallow_trace']}.
• Figure 4: Results for the shower energy reconstruction on the test dataset. The median of the uncorrected resolution is indicated as a dotted line, while the median for the corrected resolution per energy bin is shown as a solid line. The shaded areas indicate the 16th and 84th percentiles of the resolution per bin. The results for the '$\nu_x$ - NC' topology are blue while the results for the '$\nu_e$ - CC' topology are red. Left: Results for the 'shallow' station component. Right: Results for the 'deep' station component.
• Figure 5: Impact of the 'shallow' antenna SNR on the shower energy resolution for '$\nu_x$ - NC' events. Top: The maximum SNR of any of the ray tracing solutions in any of the 4 LPDA antennas plotted against the maximum SNR of any of the ray tracing solutions for the Vpol antenna. The color scale indicates the median shower energy resolution per bin, where a lighter shade of blue means a better resolution. The gray histograms indicate how many events are in each of the bins. However, this is not a physical SNR distribution as the data was generated in uniform energy bins. Bottom: The corrected median shower energy resolution per shower energy bin for different Vpol SNR bins. The number of events is shown in the plot below.