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Graph Neural Networks for Particle Reconstruction in High Energy Physics detectors

Xiangyang Ju, Steven Farrell, Paolo Calafiura, Daniel Murnane, Prabhat, Lindsey Gray, Thomas Klijnsma, Kevin Pedro, Giuseppe Cerati, Jim Kowalkowski, Gabriel Perdue, Panagiotis Spentzouris, Nhan Tran, Jean-Roch Vlimant, Alexander Zlokapa, Joosep Pata, Maria Spiropulu, Sitong An, Adam Aurisano, V Hewes, Aristeidis Tsaris, Kazuhiro Terao, Tracy Usher

arXiv:2003.11603v2physics.ins-dethep-exphysics.comp-phphysics.data-an

TL;DR

High-energy particle reconstruction must contend with sparse, high-dimensional measurements and complex detector geometry, while traditional tracking scales poorly to expected HL-LHC conditions. This paper applies graph neural networks to tracking and calorimeter clustering, reporting promising performance across both tasks, with further work needed on broader settings and capabilities.

  • Problem

    Particle tracking and calorimeter reconstruction involve sparse, high-dimensional measurements in complex detectors, and traditional sequential tracking scales poorly to expected HL-LHC event sizes.

    Source: §1 · pp. 1–2

  • Method

    The paper represents detector measurements as graph nodes, connects them using domain-informed heuristics, and trains GNNs to classify graph edges for tracking and calorimeter clustering.

    Source: §2 · p. 2, §2.2 · p. 3

  • Results

    GNNs show promising performance and scalability for both tasks: tracking relative efficiency is over 95%, while calorimeter efficiencies and purities exceed 90% even in difficult scenarios.

    Source: §4 · p. 5

  • Takeaways & Limitations

    The results support exploring GNN architectures that scale to many edges and handle multiple high-energy particle-physics reconstruction tasks.

    Source: §3 · p. 4, §4 · p. 5

    HGCal work still needs to address overlapping showers and fractional hit-energy assignment to achieve the best performance.

    Source: §3 · p. 4

Abstract

from arXiv · show

Pattern recognition problems in high energy physics are notably different from traditional machine learning applications in computer vision. Reconstruction algorithms identify and measure the kinematic properties of particles produced in high energy collisions and recorded with complex detector systems. Two critical applications are the reconstruction of charged particle trajectories in tracking detectors and the reconstruction of particle showers in calorimeters. These two problems have unique challenges and characteristics, but both have high dimensionality, high degree of sparsity, and complex geometric layouts. Graph Neural Networks (GNNs) are a relatively new class of deep learning architectures which can deal with such data effectively, allowing scientists to incorporate domain knowledge in a graph structure and learn powerful representations leveraging that structure to identify patterns of interest. In this work we demonstrate the applicability of GNNs to these two diverse particle reconstruction problems.

1 Introduction

Particle reconstruction at large, geometrically complex detectors is a challenging pattern-recognition problem, and expected HL-LHC data volumes put pressure on traditional tracking. The paper investigates GNNs for tracking and calorimeter shower reconstruction.

1 Introduction

  • High-energy collision reconstruction uses complex, sparse, high-dimensional data from detectors such as ATLAS and CMS.The detectors are described as 40 m long and 25 m in diameter.Source: §1 · pp. 1–2
  • HL-LHC is expected to increase collision data rates and volumes, challenging current reconstruction solutions.The detector tasks include reconstructing charged-particle trajectories from tracking hits and particle showers from calorimeter clusters.Source: §1 · p. 2
  • Traditional Kalman-guided tracking is sequential and scales poorly to expected HL-LHC events with O(10^4) particles and O(10^5) hits.The anticipated challenge of applying traditional tracking to HL-LHC data motivated the HEP.TrkX project to investigate deep learning solutions.Source: §1 · p. 2
  • The paper applies GNNs to particle track and shower reconstruction, extending prior particle-tracking and particle-classification studies.The introduction cites earlier GNN studies for tracking [10], and particle and event classification [3] [15] [7].Source: §1 · p. 2

2 Methodology

The methodology represents detector measurements as graph nodes and uses domain-informed edges for GNN edge classification. It applies this approach to tracking and calorimeter clustering with task-specific graph construction.

2 Methodology

  • Detector measurements become graph nodes, domain-informed heuristics create edges, and an Interaction Networks-based GNN classifies those edges.This shared representation is used for both tracking and calorimeter clustering.Source: §2 · p. 2

2.1 Tracking

  • For tracking, barrel hits are nodes and filtered connections between adjacent layers are edges, with coordinate features and same-track labels.The filter is tuned for efficiency on high-transverse-momentum tracks; node features are (r, φ, z), edge features are (∆η, ∆φ), and labels are 1 for hits from the same track and 0 otherwise.Source: §2.1 · p. 2
  • The tracking GNN encodes node and edge features, updates them through message passing, then outputs edge scores; eight graph iterations performed best.The graph module concatenates initial latent features at each iteration, a shortcut found to improve performance.Source: §2.1 · p. 2, Figure 1 · p. 3

2.2 Calorimeter clustering

  • Calorimeter graph edges can encode particle type as well as true-or-false labels, while this work focuses on static graph networks.The paper describes the calorimeter output graph as a mesh on a point cloud, from which energy clusters can be identified.Source: §2.2 · pp. 2–3
  • Calorimeter clustering applies edge classification to a static kNN graph, using EdgeConv and intermediate hidden-state concatenation.The k value ensures at least one true edge between hits in a truth-level cluster; smaller k can reduce clustering efficiency, and the tested range is 8–24 depending on noise suppression. The hidden-state concatenation improved convergence by about a factor of two versus no shortcuts.Source: §2.2 · p. 3, Figure 2 · p. 3

3 Results

The GNN approach reports strong tracking and calorimeter-clustering results, while the described evaluations and ongoing work leave clear scope boundaries. Tracking combines edge classification with a simple connecting-the-dots procedure; calorimeter tests cover individual particle samples.

3 Results

  • Tracking work targets whole-detector coverage and recovery of efficiency lost in CTD post-processing; calorimeter work targets simultaneous particle types and overlapping showers.Fractional assignment of calorimeter-hit energy to clusters is also identified as necessary for best HGCal performance; LArTPC deployment explorations are at an initial stage.Source: §3 · pp. 3–5
  • At a 0.5 score threshold, tracking edge efficiency is 95.9% and purity is 95.7%; GNN plus CTD reconstructs about 95% of graph-reconstructible tracks from 100 MeV to 5 GeV.Above 5 GeV, the passage reports insufficient statistics; the edge-score and purity/efficiency curves are shown in Figure 3.Source: §3 · p. 3, Figure 3 · p. 4
  • Muon clustering reaches 99% efficiency and 90% purity, photon clustering reaches 99% for both, and pion clustering exceeds 90% for both.The study reports these results separately for muon, photon, and pion energy deposits in CMS HGCal; pion showers are described as the most difficult because their transverse profiles vary with depth.Source: §3 · p. 4
  • Calorimeter measurements use dedicated single-particle samples; variable multiparticle final states, including τ decays and jets, are next tests.The results include separate samples for each particle type.Source: §3 · p. 4
  • The authors see potential for GNNs to scale to many edges and serve multiple reconstruction tasks, helping computing centers target acceleration resources.This is presented as a potential consequence, not as a demonstrated resource-allocation result.Source: §3 · p. 4

4 Conclusion

The paper finds GNNs suitable for tracking and calorimetry, with promising physics performance and scalability. Track finding exceeds 95% relative efficiency for all particles, while tested calorimeter clustering problems achieve efficiencies and purities above 90% even in the most difficult scenarios.

  • Over 95% relative efficiency for all particles is achieved by GNNs combined with a simple connecting-the-dot algorithm for track finding.The authors note that ongoing work is recovering inefficiency introduced by each selection.Source: §4 · p. 5
  • Efficiencies and purities are better than 90% even in the most difficult tested calorimeter clustering scenarios.The authors also report excellent energy collection efficiency.Source: §4 · p. 5
  • GNNs on Point Clouds are suitable for both tracking and calorimetry, with promising physics performance and good scalability.Source: §4 · p. 5
  • The next step for calorimetry is to connect calorimeter energy deposits and derive useful physics quantities from them.Source: §4 · p. 5
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