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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 61 , Issue 10 : 101007(2018) https://doi.org/10.1007/s11433-018-9233-5

Signal-background discrimination with convolutional neural networks in the PandaX-III experiment using MC simulation

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  • ReceivedMar 12, 2018
  • AcceptedApr 19, 2018
  • PublishedAug 9, 2018
PACS numbers

Abstract


Acknowledgment

This work was supported by the Ministry of Science and Technology of China (Grant No. 2016YFA0400302), and the National Natural Science Foundation of China (Grant Nos. 11505122, and 11775142). We thank the support from the Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education. This work was supported in part by the Chinese Academy of Sciences Center for Excellence in Particle Physics (CCEPP).


Supplement

Appendix

The ambiguity of position reconstruction with strip readout

The MicroMegas modules used by PandaX-III are read out with strips. Simultaneously hits on different strips can be used to reconstructed the positions of the signal. But ambiguity appears when more than 2 strips are fired at the same time, and an example is visualized in Figure A1.

Comparison between three CNN models

We have tested several different CNN structures for the discrimination of signal and background with a smaller training data set. A comparison between the model complexity, best training accuracy and the signal efficiency at a fixed background rejection efficiency for the testing data is given in tab:comparison. The ResNet-50 is finally chosen due to its highest signal efficiency.


References

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  • Figure 1

    (Color online) A cross-sectional view of the simulated PandaX-III detector.

  • Figure 2

    (Color online) The number of electrons hitting a readout plane in an event by time. The bin width is 20 ns. Time 0 is defined as the time when the first electron reaches the readout plane. The time series between the start point and the end point are finally recorded.

  • Figure 3

    (Color online) Examples of mapping from recorded events to images. Top: $^{136}$Xe NLDBD event; Bottom: gamma background event from $^{214}$Bi. (a) and (d), the raw Monte Carlo 3D hits map; (b) and (e), the $x$-$z$ and $y$-$z$ projection of the event after reconstruction. (c) and (f), the resulting images for training. For better visualization, color inversion and enhancement were applied to the final images. The cyan color stands for the red channel, and the magenta color for the green channel.

  • Figure 4

    (Color online) The evolution of the training/validation accuracy with epochs.

  • Figure 5

    (Color online) The distributions of $\kappa$ for NLDBD signals (red) and high energy gamma backgrounds (blue) from model-16 in testing dataset. The rising of $\kappa$ for backgrounds is resulted from the signal-like background events.

  • Figure 6

    (Color online) (a) The signal efficiency $\epsilon_{s,\text{cnn}}$ (red) and the background rejection efficiency $1-\epsilon_{b,\text{cnn}}$ (blue) as a function of $\kappa_c$ from model-16; (b) the efficiency ratio $\epsilon_{s,\text{cnn}}/\sqrt{\epsilon_{b,\text{cnn}}}$ as a function of $\kappa_c$ from model-16. The optimized $\kappa_c$ is plotted as a green dashed line.

  • Figure 7

    (Color online) The background rejection efficiency $1-\epsilon_{b,\text{cnn}}$ versus the signal efficiency $\epsilon_{s,\text{cnn}}$ from model-16.

  • Figure 8

    (Color online) The reconstructed energy spectra of signal and backgrounds before and after the optimal cut $\kappa_c$ from model-16. (a) NLDBD signal events; (b) background events from $^{214}$Bi. The spectra are not normalized.

  • Figure 9

    (Color online) Falsely identified events by CNN in epoch 16. (a) The $x$-$z$ and $y$-$z$ projection of a NLDBD signal event, which is identified as a background event; (b) the $x$-$z$ and $y$-$z$ projection of a background event, which is identified as a signal event.

  • Table 1   The structure of the modified ResNet-50. The “repetition” column indicates the numberof times the block appears in the network, and the default value is 1
    Layer name Layer type Output tensor Layer attribute Repetition
    Input_1 InputLayer 240, 240, 3
    Conv1 block Convolution2D 120, 120, 64 7$\times$7, 64
    Pooling MaxPooling2D 59, 59, 64
    Convolution2D 59, 59, 64 1$\times$1, 64
    Conv2 block Convolution2D 59, 59, 64 3$\times$3, 643
    Convolution2D 59, 59, 256 1$\times$1, 256
    Convolution2D 30, 30, 128 1$\times$1, 128
    Conv3 block Convolution2D 30, 30, 128 3$\times$3, 128 4
    Convolution2D 30, 30, 512 1$\times$1, 512
    Convolution2D 15, 15, 256 1$\times$1, 256
    Conv4 block Convolution2D 15, 15, 256 3$\times$3, 2566
    Convolution2D 15, 15, 1024 1$\times$1, 1024
    Convolution2D 8, 8, 512 1$\times$1, 512
    Conv5 block Convolution2D 8, 8, 512 3$\times$3, 512 3
    Convolution2D 8, 8, 2048 1$\times$1, 2048
    Pooling AveragePooling2D 1, 1, 2048
    Flatten Flatten 2048
    Dense Dense 256 Relu
    Dropout Dropout 256
    Dense Dense 1 Sigmoid
  • Table A1   Simple comparison between different CNN models with a smaller training dataset.The signal efficiency $\epsilon_{s}$ is calculated at a fixed background rejection efficiency of $98.0%$
    Model Number of Accuracy (%) $\epsilon_{s}$ (%)
    trainable parameters
    3-Layer 720993 82 35.7
    convolutional model
    VGG-16 [25] $15894849$ 92.8 73.9
    ResNet-50 $24059393$ 94.0 79.0
  • Table 2   The optimized $\kappa_c$, corresponding signal efficiency $\epsilon_{s,\text{cnn}}$, background rejection efficiency $1~-~\epsilon_{b,\text{cnn}}$, the ratio of $\epsilon_{s,\text{cnn}}/\sqrt{\epsilon_{b,\text{cnn}}}$ and final BI (count kg$^{-1}~$ keV$^{-1}$ year$^{-1}$). The BI before theCNN discrimination is $3.088\times10^{-3}$ count kg$^{-1}$ keV$^{-1}$ year$^{-1}$
    Epoch Optimized $\kappa_c$ $\epsilon_{s,\text{cnn}}$ $~1-\epsilon_{b,\text{cnn}}$ $\epsilon_{s,\text{cnn}}/\sqrt{\epsilon_{b,\text{cnn}}}$ Final BI
    16 0.983 0.475 0.9943 6.264 $1.775\times10^{-5}$
    17 0.976 0.569 0.9916 6.196 $2.605\times10^{-5}$
    18 0.981 0.487 0.9936 6.098 $1.968\times10^{-5}$
    19 0.966 0.540 0.9923 6.165 $2.369\times10^{-5}$
    20 0.976 0.520 0.9928 6.145 $2.215\times10^{-5}$
    Average $6.174\pm0.055$
  • Table 3   Comparison between the results from PandaX-III baseline requirement and the CNN method
    PandaX-III baseline CNN (model-16) CNN (model-18) CNN (average)
    $\epsilon_{s}$ 0.645 0.475 0.487
    $~1-\epsilon_{b}$ 0.9714 0.9943 0.9936
    $\epsilon_{s}/\sqrt{\epsilon_{b}}$ 3.816 6.264 6.098 6.174
    Improvement $64.2%$ $59.8%$ $61.8%$