Label-free timing analysis of modularized nuclear 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 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.

PulseDL-II: A System-on-Chip Neural Network Accelerator for Timing and Energy Extraction of Nuclear Detector Signals

Front-end electronics equipped with high-speed digitizers are being used and proposed for future nuclear detectors. Recent literature reveals that deep learning models, especially one-dimensional convolutional neural networks, are promising when dealing with digital signals from nuclear detectors. Simulations and experiments demonstrate the satisfactory accuracy and additional benefits of neural networks in this area. However, specific hardware accelerating such models for online operations still needs to be studied. In this work, we introduce PulseDL-II, a system-on-chip (SoC) specially designed for applications of event feature (time, energy, etc.) extraction from pulses with deep learning. Based on the previous version, PulseDL-II incorporates a RISC CPU into the system structure for better functional flexibility and integrity. The neural network accelerator in the SoC adopts a three-level (arithmetic unit, processing element, neural network) hierarchical architecture and facilitates parameter optimization of the digital design. Furthermore, we devise a quantization scheme and associated implementation methods (rescale & bit-shift) for full compatibility with deep learning frameworks (e.g., TensorFlow) within a selected subset of layer types. With the current scheme, the quantization-aware training of neural networks is supported, and network models are automatically transformed into software of RISC CPU by dedicated scripts, with nearly no loss of accuracy. We validate PulseDL-II on field programmable gate arrays (FPGA). Finally, system validation is done with an experimental setup made up of a direct digital synthesis (DDS) signal generator and an FPGA development board with analog-to-digital converters (ADC). The proposed system achieved 60 ps time resolution and 0.40% energy resolution with online neural network inference at signal to noise ratio (SNR) of 47.4 dB.