Optimised neural networks for online processing of ATLAS calorimeter data on FPGAs

TL;DR

This work tackles energy reconstruction for ATLAS LAr calorimeter cells under HL-LHC pile-up by deploying FPGA-compatible neural networks. Through Bayesian hyperparameter optimisation, Dense, CNN, and combined Dense+RNN architectures achieve about $80~\mathrm{MeV}$ energy resolution, outperforming the current optimal filtering method and comparable RNNs while staying under hardware limits. The Dense architecture is extended with Deep Evidential Regression to provide per-event uncertainties via a Normal–Inverse–Gamma distribution, with epistemic uncertainty dominating and overall uncertainties consistent with prediction residuals. The results demonstrate feasible, low-latency FPGA implementations that improve energy scale accuracy and supply reliable uncertainty estimates for clustering and trigger decision-making in HL-LHC conditions.

Abstract

A study of neural network architectures for the reconstruction of the energy deposited in the cells of the ATLAS liquid-argon calorimeters under high pile-up conditions expected at the HL-LHC is presented. These networks are designed to run on the FPGA-based readout hardware of the calorimeters under strict size and latency constraints. Several architectures, including Dense, Recurrent (RNN), and Convolutional (CNN) neural networks, are optimised using a Bayesian procedure that balances energy resolution against network size. The optimised Dense, CNN, and combined Dense+RNN architectures achieve a transverse energy resolution of approximately 80 MeV, outperforming both the optimal filtering (OF) method currently in use and RNNs of similar complexity. A detailed comparison across the full dynamic range shows that Dense, CNN, and Dense+RNN accurately reproduce the energy scale, while OF and RNNs underestimate the energy. Deep Evidential Regression is implemented within the Dense architecture to address the need for reliable per-event energy uncertainties. This approach provides predictive uncertainty estimates with minimal increase in network size. The predicted uncertainty is found to be consistent, on average, with the difference between the true deposited energy and the predicted energy.

Figures (10)

• Figure 1: The CNN architecture with 3 convolutional layers with kernels sliding in the time directions to compute the deposited energy at each BC. Only the final filter operations at each layer are computed at each BC, the previous filter results, represented with the grey connections, are reused from previous BCs
• Figure 2: The RNN architecture, where an RNN sequence is used to process the samples sequence, followed by a final dense layer computing the transverse energy
• Figure 3: The Dense+RNN architecture, where a dense layer processes pre-deposit samples to initialize an RNN sequence for post-deposit samples, followed by a final dense layer computing the transverse energy
• Figure 4: The Staged Dense architecture, where a First Dense block processes pre-deposit samples, the Main Dense combines this output with post-deposit samples, and the Final Dense outputs the transverse energy
• Figure 5: Transverse energy resolution and number of multiply–accumulate (MAC) units for the Dense neural network architecture as a function of the evaluation number corresponding to a given hyperparameter set in an iterative Bayesian optimisation process. The best model up to each evaluation is shown, selected based on a score balancing energy resolution with the number of MAC units to achieve an optimal trade-off between resolution and network size. The resolution is computed for a single cell of the LAr calorimeter barrel section (EMB) for a dataset with pile-up of $\langle\mu\rangle=200$