Real-time graph neural networks on FPGAs for the Belle II electromagnetic calorimeter

We present the development and evaluation of a real-time Graph Neural Network-based trigger module for the electromagnetic calorimeter of the Belle II experiment at the SuperKEKB collider. The algorithm processes calorimeter trigger cells as graph nodes to perform clustering, feature extraction, and per-cluster signal classification with deterministic latency. The model predicts cluster positions and energies and provides a signal classification score, enabling a more flexible clustering strategy than the baseline trigger algorithm. Implemented on an FPGA and integrated into the Belle II trigger readout infrastructure for synchronous operation, the system sustains the 8 MHz trigger throughput with an end-to-end latency of 3.168 μs. The performance is evaluated on simulated events and collision data. The energy resolution is comparable to the baseline trigger, while the position resolution for high-energy clusters improves by up to 18 % in the central detector region. Cluster purity increases by up to 20 % at low energies for isolated clusters, and cluster efficiency improves by up to 20 % for overlapping clusters. The signal classifier enables additional background suppression at fixed signal retention. These results demonstrate a first step towards GNN-based real-time reconstruction on FPGAs in a collider trigger. While the end-to-end latency exceeds the trigger decision budget, the system already sustains full operational conditions with 100 % uptime.