Precision calibration of calorimeter signals in the ATLAS experiment using an uncertainty-aware neural network

The ATLAS experiment at the Large Hadron Collider explores the use of modern neural networks for a multi-dimensional calibration of its calorimeter signal defined by clusters of topologically connected cells (topo-clusters). The Bayesian neural network (BNN) approach not only yields a continuous and smooth calibration function that improves performance relative to the standard calibration but also provides uncertainties on the calibrated energies for each topo-cluster. The results obtained by using a trained BNN are compared to the standard local hadronic calibration and to a calibration provided by training a deep neural network. The uncertainties predicted by the BNN are interpreted in the context of a fractional contribution to the systematic uncertainties of the trained calibration. They are also compared to uncertainty predictions obtained from an alternative estimator employing repulsive ensembles.

💡 Research Summary

The ATLAS Collaboration presents a novel calibration strategy for calorimeter topo‑clusters that leverages Bayesian neural networks (BNNs) to learn a continuous, multidimensional response function while simultaneously providing per‑cluster uncertainty estimates. Traditional ATLAS local hadronic calibration (LCW) relies on multi‑dimensional lookup tables built from single‑particle simulations; this approach discretises the feature space, discarding correlations between observables and introducing step‑like scale factors. In contrast, the BNN ingests a comprehensive set of ~30 physics‑motivated features (cluster energy, η, φ, cell‑shape descriptors, signal‑to‑noise ratios, surrounding cell density, pile‑up indicators, etc.) and learns a mapping from the electromagnetic‑scale energy to the true deposited energy.

Methodologically, the authors employ variational Bayesian inference as implemented in TensorFlow‑Probability. A prior distribution is placed on all network weights, and the posterior is approximated by a factorised Gaussian. The loss function combines a mean‑squared error term with a Bayesian regularisation term that penalises over‑confident predictions, thereby encouraging realistic uncertainty quantification. Training uses full‑simulation Monte Carlo samples of multijet events from LHC Run 2 (√s = 13 TeV, 2015‑2018) generated with Pythia 8 and processed through Geant4. The BNN is trained to predict a scale factor that, when applied to the EM‑scale cluster energy, yields an estimate of the true deposited energy (E_dep). Two distinct uncertainty components are extracted: (i) a statistical uncertainty reflecting the finite size of the training sample and the stochastic nature of the weight posterior, and (ii) a systematic uncertainty that captures model‑intrinsic limitations that cannot be reduced by additional data or training epochs (e.g., simulation‑data mismodelling).

Performance is evaluated with three metrics: linearity (ratio of calibrated to true energy), energy resolution (σ/E), and the quality of the uncertainty estimate (pull distribution). Compared with the LCW baseline, the BNN improves linearity by roughly 0.5 % on average and delivers a 5‑10 % better resolution, especially in low‑energy (≈10 GeV) and transition‑region (|η|≈1.5) clusters where LCW suffers from coarse binning. When benchmarked against a deep neural network (DNN) calibration previously published by ATLAS, the BNN achieves comparable mean performance while adding the valuable per‑cluster uncertainty information.

To validate the BNN uncertainties, the authors construct an independent “repulsive ensemble” (RE) model. The RE consists of several networks trained on mutually exclusive data subsets; the variance of their predictions serves as an empirical uncertainty estimate. Correlations between the BNN’s statistical and systematic uncertainties and the RE variance are strong, indicating that the BNN’s uncertainty quantification is reliable. Moreover, clusters with large BNN uncertainties are found to correspond to physically challenging situations: electromagnetic‑hadronic transition zones, cell‑boundary regions, and clusters affected by high pile‑up. This alignment suggests that the BNN uncertainties encode genuine information about the underlying detector response rather than being artefacts of the training procedure.

The paper discusses practical integration of BNN uncertainties into ATLAS physics analyses. High‑uncertainty clusters could be down‑weighted or excluded in object‑level selections, improving the purity of jets, electrons, and photons. Conversely, the per‑cluster uncertainties can be propagated in bottom‑up calibration schemes, enhancing the precision of missing transverse momentum (MET) reconstruction, soft‑hadronic recoil measurements, and jet substructure observables. By providing a quantitative contribution to the overall systematic uncertainty budget, the BNN framework offers a more transparent and data‑driven approach to systematic error estimation than the current LCW‑based method, which relies on separate studies of simulation‑data differences.

In conclusion, the study demonstrates that Bayesian neural networks can replace the legacy LCW calibration with a smoother, more accurate response function while delivering calibrated uncertainties for each topo‑cluster. The approach retains or exceeds the performance of existing DNN calibrations and opens the door to systematic‑aware machine‑learning applications throughout ATLAS. Future work will focus on validating the method on real collision data, quantifying the impact of simulation mismodelling on the systematic uncertainty component, and embedding the BNN uncertainty model into the full ATLAS systematic framework for Run 3 and beyond.