Pulse timing is an important topic in nuclear instrumentation, with far-reaching applications from high energy physics to radiation imaging. While high-speed analog-to-digital converters become more and more developed and accessible, their potential uses and merits in nuclear detector signal processing are still uncertain, partially due to associated timing algorithms which are not fully understood and utilized. In this paper, we propose a novel method based on deep learning for timing analysis of modularized nuclear detectors without explicit needs of labelling event data. By taking advantage of the inner time correlation of individual detectors, a label-free loss function with a specially designed regularizer is formed to supervise the training of neural networks towards a meaningful and accurate mapping function. We mathematically demonstrate the existence of the optimal function desired by the method, and give a systematic algorithm for training and calibration of the model. The proposed method is validated on two experimental datasets. In the toy experiment, the neural network model achieves the single-channel time resolution of 8.8 ps and exhibits robustness against concept drift in the dataset. In the electromagnetic calorimeter experiment, several neural network models (FC, CNN and LSTM) are tested to show their conformance to the underlying physical constraint and to judge their performance against traditional methods. In total, the proposed method works well in either ideal or noisy experimental condition and recovers the time information from waveform samples successfully and precisely.

翻译：脉冲时序是核仪器领域的重要课题，在高能物理到辐射成像等多个领域具有广泛影响。尽管高速模数转换器日益成熟且易于获取，但其在核探测器信号处理中的潜在用途和优势仍不明确，部分原因在于相关的时序算法尚未得到充分理解和利用。本文提出一种基于深度学习的新方法，用于模块化核探测器的时序分析，无需对事件数据进行显式标记。通过利用单个探测器内部的时间相关性，我们构建了一个带有特殊设计正则化项的无标记损失函数，以监督神经网络学习有意义且准确的映射函数。我们从数学上证明了该方法所寻求的最优函数存在性，并给出了系统的模型训练与校准算法。该方法在两个实验数据集上得到验证。在模拟实验中，神经网络模型实现了8.8 ps的单通道时间分辨率，并对数据集中的概念漂移表现出鲁棒性。在电磁量能器实验中，我们测试了多种神经网络模型（全连接网络、卷积神经网络和长短期记忆网络），验证其与底层物理约束的一致性，并评估其相对于传统方法的性能。总体而言，所提方法在理想或噪声实验条件下均表现良好，能成功且精确地从波形样本中恢复时间信息。