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：脉冲定时是核仪器领域的重要课题，在高能物理及辐射成像等领域具有广泛应用。尽管高速模数转换器发展迅速且日益普及，其在核探测器信号处理中的潜在用途与优势仍不明确，部分原因在于相关定时算法尚未被充分理解与利用。本文提出一种基于深度学习的模块化核探测器定时分析方法，无需显式标注事件数据。通过利用单个探测器的内部时间相关性，设计了一种带特殊正则化项的无标记损失函数，引导神经网络训练生成有意义且精确的映射函数。我们从数学上论证了该方法所需最优函数的存在性，并给出了模型训练与标定的系统算法。该方法在两个实验数据集上得到了验证。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）以验证其与潜在物理约束的一致性，并与传统方法进行性能比较。总体而言，该方法在理想或噪声实验条件下均表现良好，能够成功且精确地从波形样本中恢复时间信息。