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

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 labeling 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 (NNs) 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 as main transducers. In the toy experiment, the NN 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 NN models (fully-connected, convolutional neural network and long short-term memory) 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.