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 detectors without explicit needs of labelling event data. By taking advantage of the intrinsic time correlations, 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 based on silicon photomultipliers (SiPM) as main transducers. 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：脉冲定时是核仪器领域的重要课题，在高能物理到辐射成像等众多领域具有深远应用。尽管高速模数转换器日益成熟和普及，但其在核探测器信号处理中的潜在用途和优势仍不明确，部分原因在于相关定时算法尚未得到充分理解和应用。本文提出一种基于深度学习的模块化探测器时序分析方法，无需对事件数据进行显式标注。通过利用内在时间相关性，构建了带有特殊设计正则化项的无标签损失函数，以监督神经网络训练得到具有物理意义且准确的映射函数。我们从数学上证明了该方法所期望的最优函数的存在性，并给出了系统的模型训练与校准算法。该方法在以硅光电倍增管（SiPM）为主要换能器的两组实验数据集上得到验证。在玩具实验中，神经网络模型实现了8.8皮秒的单通道时间分辨率，并展现出对数据集概念漂移的鲁棒性。在电磁量能器实验中，测试了全连接网络（FC）、卷积神经网络（CNN）和长短期记忆网络（LSTM）等多种神经网络模型，验证了其与底层物理约束的一致性，并评估了其相对于传统方法的性能。总体而言，该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。