Neural Networks for 3D Characterisation of AGATA Crystals

Precise localisation of gamma-ray interactions is crucial for the performance of the Advanced GAmma Tracking Array (AGATA). The Pulse Shape Analysis (PSA) method used for the position estimation of gamma-ray interactions relies on a simulated signal database. The Pulse Shape Comparison Scanning (PSCS) method was used to scan AGATA crystals in order to produce an experimental database of signals. This paper presents a novel approach using Long Short-Term Memory (LSTM) neural networks to determine the 3D interaction position of gamma rays within AGATA crystals, trained on data from IPHC Strasbourg, allowing for the construction of an experimental database. A custom masked loss function is introduced to enable training with incomplete position information. The database generated by this new method outperforms the existing simulated database, and the experimental database obtained from the conventional PSCS algorithm.

💡 Research Summary

The paper addresses a central challenge in the Advanced GAmma Tracking Array (AGATA): the precise three‑dimensional localisation of γ‑ray interaction points inside high‑purity germanium (HPGe) crystals. Traditional Pulse Shape Analysis (PSA) relies on a simulated signal library, while the Pulse Shape Comparison Scanning (PSCS) technique builds an experimental library by scanning crystals with a collimated source. PSCS, however, is computationally intensive (≈4.7 days per crystal) and requires careful χ² threshold tuning for each scan direction, limiting its scalability.

To overcome these limitations, the authors propose a machine‑learning approach that directly learns the mapping from measured detector waveforms to interaction coordinates. They use the Strasbourg scanning table data collected at the Institut pluridisciplinaire Hubert Curien (IPHC) as the training set, thereby constructing an experimental database without relying on simulations. The raw data consist of “super‑traces” – concatenated waveforms from 36 segmented contacts plus the core, each sampled at 100 MHz. After preprocessing (compression, hit filtering, coincidence removal, timing alignment, and reduction to the rising‑edge/plateau region), each event is represented by 37 × 60 = 2220 features.

Because each scan provides only two of the three spatial coordinates (vertical scans give X and Y, horizontal scans give X and Z), the authors introduce a masked Euclidean loss. For a given training sample the loss is computed only on the known axes, with binary masks Mx, My, Mz indicating which components are present. This enables back‑propagation despite incomplete ground truth, while during inference the network predicts all three coordinates.

The neural network architecture is built around Long Short‑Term Memory (LSTM) layers, chosen for their ability to capture temporal dependencies in the waveform sequence. The 2220‑dimensional input is reshaped to (37, 60), then permuted to (60, 37) so that the 60 time samples become the sequence dimension. Two stacked LSTM layers (each with 500 hidden units) process the sequence, followed by four dense layers (200, 100, 100, 100 neurons) with ReLU activation, and a final linear layer outputting (x̂, ŷ, ẑ). Gaussian noise is added to the input during training to improve robustness.

A key practical issue is the highly non‑uniform distribution of events across the 36 crystal segments and across depth layers. Training a single global model caused bias toward heavily populated regions. The authors evaluated three strategies: (i) training on a uniformly subsampled dataset (which reduced data to 2 % and degraded performance), (ii) balanced‑batch training (some improvement), and (iii) training separate models per segment. The per‑segment approach yielded the lowest average error and mitigated the bias, so all subsequent results use 36 independent models, each trained only on events where its segment is the fired one.

Training employed the Adam optimizer (learning rate 1e‑4), batch size 500, and 30 000 iterations per model. Waveforms were normalized so that the peak amplitude equals 1000 arbitrary units, a standard AGATA PSA practice that assumes shape independence from deposited energy. The validation set (10 % of data) was drawn from the same energy windows (300‑480 keV Compton continuum and 650‑670 keV photopeak) that showed the lowest intrinsic PSA errors.

Performance evaluation shows that the LSTM‑based experimental database achieves an average position error of ≈0.9 mm, a 30‑40 % improvement over both the simulated ADL library and the conventional PSCS‑derived database. Moreover, the total training time per segment is on the order of a few hours on a single GPU, compared with the multi‑day processing required by the traditional PSCS algorithm. Error analysis reveals larger uncertainties for rear depth layers (5‑6) and for sectors that receive attenuated beams during scanning, but the per‑segment training largely compensates for these effects.

In summary, the paper contributes three major innovations to AGATA detector characterisation: (1) direct use of experimentally measured waveforms to build a position‑reconstruction database, eliminating reliance on potentially inaccurate simulations; (2) a masked loss function that enables learning from partially labelled data; and (3) a segment‑wise modelling strategy that resolves data‑distribution bias. The approach demonstrates superior spatial resolution, dramatically reduced processing time, and scalability to future detector arrays. The authors suggest extensions to multi‑interaction events, real‑time tracking, and other crystal geometries (types B and C) as promising directions for further research.