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We provide a fast approach incorporating the usage of deep learning for studying the effects of the number of photon sensors in an antineutrino detector on the event reconstruction performance therein. This work is a first attempt to harness the power of deep learning for detector designing and upgrade planning. Using the Daya Bay detector as a case study and the vertex reconstruction performance as the objective for the deep neural network, we find that the photomultiplier tubes (PMTs) at Daya Bay have different relative importance to the vertex reconstruction. More importantly, the vertex position resolutions for the Daya Bay detector follow approximately a multiexponential relationship with respect to the number of PMTs and, hence, the coverage. This could also assist in deciding on the merits of installing additional PMTs for future detector plans. The approach could easily be used with other objectives in place of vertex reconstruction.

The choice of photon sensors such as photomultiplier tubes (PMTs), be it their expected sizes, locations, and the total number of sensors in antineutrino detectors, including Daya Bay [

The Daya Bay antineutrino detectors are liquid scintillator detectors with a physics program focusing on the precision measurement of the neutrino mixing angle

As aforementioned, we used deep learning to perform the IBD vertex reconstruction in order to study the effects of PMTs on an event reconstruction. Deep learning is a class of machine learning, which is especially adept at leveraging large datasets to compute human-comprehensible quantities by learning the various degrees of correlations within. Notably, it can, on its own, learn to discover functional relationships from the data without

The ubiquity of deep learning and its significant success over traditional methods across disparate fields [

As mentioned in Section

Let the true position of the IBD prompt events be

In our approach utilizing DNNs, we used a Monte Carlo dataset comprising 2 million IBD prompt events obtained from a Daya Bay detector model which were randomly partitioned into a training set (1.4 million), a validation set (0.3 million), and a test set (0.3 million). The validation set is used for the early stopping of the DNN training to prevent overfitting or underfitting of the data [

The efficacy of deep learning to predict the position of the IBD prompt events can be demonstrated by the residual distributions shown in Figure

Residual distributions for x and z using all 192 PMT charge information.

A straightforward and brute force use of (

This fast approach integrates a DNN component from the autoencoder architecture [

DNN architecture consisting of a bottleneck neuron.

The heatmap in Figure

Resolution

In Figure

Weights as given by the bottleneck neuron corresponding to each PMT for (a)

Resolution

Weights as given by the bottleneck neuron corresponding to using a second candidate PMT, and the most important PMT,

Figure

Residual curves for

In this work, we provide a fast approach using a deep neural network with a bottleneck neuron to uncover the effects of the number of photon sensors such as PMTs on the vertex resolutions in an antineutrino detector. The results have been compared with a random PMT search and a brute force search which yields the ideal result. Our inputs are the simulated charge information of the Daya Bay PMTs. The fast approach produces results close to those from the brute force search and fares much better than a random search. We find that the vertex resolution of the event reconstruction at the Daya Bay is approximately a multiexponentially decreasing function with respect to the number of PMTs and hence, also, the coverage. In future work, we envisage the possibility of incorporating the temporal information, i.e., the time of arrival of each photon in addition to the charge information to reconstruct the vertices. In addition, one could also study the size of the PMT needed alongside its installation location corresponding to the best event vertex reconstruction resolution. Also, a subsequent work from here would be the study of the effect of PMTs based on the event energy upon obtaining the vertex positions. Although studying the energy might need modifications to the deep network as the energy is a positive-definite quantity, the energy resolution is important when considering physics sensitivity and thereby also impacting the design of future antineutrino detectors including JUNO.

In order to use the bottleneck DNN approach for new detectors in designing phases, we suggest Monte Carlo simulations using various

The data used to support the findings of this study are available from the corresponding author upon request.

Zhi-Qiang Qian is co-first author.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors thank Shen-Jian Chen and Zuo-Wei Liu for their computing facilities and helpful discussions. They would also like to thank Chao Zhang, Zhe Wang, Samuel Kohn, the Daya Bay ACC, and the Collaboration for their time and comments. This work was supported by the National 973 Project Foundation of the Ministry of Science and Technology of China (Contract no. 2013CB834300) and the International Science & Technology Cooperation Program of China (Contract No. 2015DFG02100).

_{13}with the Double Chooz detector