  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.
