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Pulse timing is an important topic in nuclear instrumentation, withfar-reaching applications from high energy physics to radiation imaging. Whilehigh-speed analog-to-digital converters become more and more developed andaccessible, their potential uses and merits in nuclear detector signalprocessing are still uncertain, partially due to associated timing algorithmswhich are not fully understood and utilized. In this paper, we propose a novelmethod based on deep learning for timing analysis of modularized detectorswithout explicit needs of labelling event data. By taking advantage of theintrinsic time correlations, a label-free loss function with a speciallydesigned regularizer is formed to supervise the training of neural networkstowards a meaningful and accurate mapping function. We mathematicallydemonstrate the existence of the optimal function desired by the method, andgive a systematic algorithm for training and calibration of the model. Theproposed method is validated on two experimental datasets based on siliconphotomultipliers (SiPM) as main transducers. In the toy experiment, the neuralnetwork model achieves the single-channel time resolution of 8.8 ps andexhibits robustness against concept drift in the dataset. In theelectromagnetic calorimeter experiment, several neural network models (FC, CNNand LSTM) are tested to show their conformance to the underlying physicalconstraint and to judge their performance against traditional methods. Intotal, the proposed method works well in either ideal or noisy experimentalcondition and recovers the time information from waveform samples successfullyand precisely.

Label-free timing analysis of SiPM-based modularized detectors with physics-constrained deep learning