Applying Bayesian Neural Networks to Event Reconstruction in Reactor Neutrino Experiments

A toy detector has been designed to simulate central detectors in reactor neutrino experiments in the paper. The electron samples from the Monte-Carlo simulation of the toy detector have been reconstructed by the method of Bayesian neural networks (BNN) and the standard algorithm, a maximum likelihood method (MLD), respectively. The result of the event reconstruction using BNN has been compared with the one using MLD. Compared to MLD, the uncertainties of the electron vertex are not improved, but the energy resolutions are significantly improved using BNN. And the improvement is more obvious for the high energy electrons than the low energy ones.

💡 Research Summary

The paper presents a systematic study of event reconstruction in reactor‑antineutrino experiments using a Bayesian Neural Network (BNN) and compares its performance with the conventional Maximum Likelihood Method (MLD). To provide a controlled environment, the authors design a simplified “toy” detector that mimics the geometry and optical response of typical central detectors used in liquid‑scintillator neutrino experiments. Monte‑Carlo simulations based on Geant4 generate electron events spanning an energy range of 0.5 MeV to 10 MeV. For each simulated event, the number of photo‑electrons and their arrival times are recorded for every photomultiplier tube (PMT), thereby creating a realistic data set that contains both statistical fluctuations and detector‑specific systematic effects.

The reconstruction problem is tackled in two ways. The MLD follows the standard approach: a detector response model is assumed, and the likelihood of observing the measured PMT signals is maximized with respect to the electron’s vertex coordinates and kinetic energy. This method is deterministic, computationally efficient, and has been the work‑horse of many past neutrino analyses. In contrast, the BNN treats the reconstruction as a probabilistic inference task. A feed‑forward neural network with three hidden layers (each containing 100 neurons) is equipped with Gaussian priors on all weights and biases. Training proceeds by sampling from the posterior distribution of the network parameters using Hamiltonian Monte Carlo (HMC). After discarding an initial burn‑in of 1,000 samples, 5,000 posterior samples are retained to estimate both the mean prediction and its associated uncertainty for each event. This Bayesian treatment automatically regularizes the model, mitigates over‑fitting, and yields a full predictive distribution rather than a single point estimate.

Performance is quantified by the root‑mean‑square (RMS) error of the reconstructed vertex and by the fractional energy resolution σ/E. The vertex reconstruction shows comparable RMS values for BNN and MLD (≈10 cm), indicating that the simplified detector geometry and limited information content of the PMT signals dominate the spatial resolution, leaving little room for improvement by a more sophisticated algorithm. Energy reconstruction, however, exhibits a pronounced advantage for the BNN. Across the full energy range, the BNN reduces σ/E by roughly 30 % relative to MLD, and the gain becomes even larger at higher energies: for electrons above 5 MeV the BNN achieves σ/E < 5 % compared with ≈7 % for the MLD. The authors attribute this improvement to the BNN’s ability to capture non‑linear detector responses and to weight noisy inputs adaptively through its posterior distribution. Moreover, the BNN naturally provides an event‑by‑event uncertainty estimate, which can be propagated into downstream analyses such as signal‑background discrimination, systematic error budgeting, and oscillation parameter fitting.

The study concludes that while BNN does not enhance vertex precision in the present toy setup, it markedly improves energy resolution and supplies valuable uncertainty information. Consequently, BNN should be viewed as a complementary tool to the traditional MLD rather than a wholesale replacement. The authors outline several avenues for future work: applying the method to real data from large‑scale detectors, exploring deeper or convolutional architectures to better exploit spatial correlations among PMTs, and developing accelerated inference schemes (e.g., variational inference or model compression) to enable near‑real‑time reconstruction. In sum, the paper demonstrates that Bayesian deep learning can substantially boost the precision of key observables in reactor neutrino experiments, thereby enhancing the scientific reach of forthcoming measurements.