Building on the pioneering work of the HEP.TrkX project , Exa.TrkX developed geometric learning tracking pipelines that include metric learning and graph networks. These end-to-end pipelines capture the relationships between spacepoint measurements belonging to a particle track. We tested the pipelines on simulated data from HL-LHC tracking detectors [2,5], Liquid Argon TPCs for neutrino experiments [3,8], and the straw tube tracker of the PANDA experiment. The HL-LHC pipeline provides state-of-the-art tracking performance (Fig. 2), scales linearly with spacepoint density (Fig. 1), and has been optimized to run end-to-end on GP-GPUs, achieving a 20x speed-up with respect to the baseline implementation [6,9].
The Exa.TrkX geometric learning approach also has shown promise in less traditional tracking applications, like large-radius tracking for new physics searches at the LHC .
Exa.TrkX also contributed to developing and optimizing common data formats for ML training and inference targeting both neutrino detectors and LHC trackers.
When applied to LArTPC neutrino experiments, the Exa.TrkX message-passing graph neural network classifies nodes, defined as the charge measurements or hits, according to the underlying particle type that produced them (Fig 3). Thanks to special 3D edges, our network can connect nodes within and across wire planes and achieve 94% accuracy with 96% consistency across wire planes .
From the very beginning, the Exa.TrkX project has functioned as a collaboration open beyond its three original institutions (CalTech, FNAL, and LBNL). We released the code associated with every publication and produced tutorials and quickstart examples to test our pipeline.
Eight US universities and six international institutions have contributed significantly to our research program and publications. The collaboration currently includes members of the ATLAS, CMS, DUNE, and PANDA experiments. Members of the FNAL muon g-2 experiment and CERN MUonE projects have tested the Exa.TrkX pipeline on their datasets.
Exa.TrkX profits from multi-year partnerships with related research projects, namely the ACTS common tracking software, the ECP ExaLearn project, the NSF A3D3 institute, and the Fast ML Lab. More recently, as our pipeline matured and became applicable to more complex datasets, we started a partnership with HPE Lab, which uses our pipeline as a benchmark for its hyperparameter optimization and common metadata framework. NVIDIA (through the NERSC NESAP program) is evaluating the Exa.TrkX pipeline as an advanced use case for their R&D in Graph neural networks optimization.
At this stage of the project, a necessary focus of the Exa.TrkX team is on consolidation and dissemination of the results obtained so far. We are re-engineering the LHC pipeline to improve its modularity and usability across experiment frameworks. We aim to integrate our pipelines with online and offline reconstruction chains of neutrino and collider detectors and release a repository of production-quality HEP pattern recognition models that can be readily composed into an experiment-specific pipeline.
We are investigating heterogeneous graph networks to improve our pipelines' physics performance and make our models more easily generalizable . Heterogeneity allows mixing and matching information from multiple detector geometries and types (strips vs. pixels, calorimeters vs. trackers vs. timing detectors, etc.).
We have demonstrated that it is possible to recover “difficult” tracks (e.g., tracks with a missing spacepoint) by using hierarchical graph networks . Next, we need to scale these models to more challenging datasets, including full HL-LHC simulations.
We are also investigating how to parallelize our pipeline across multiple GPUs. Data parallelism for graph networks is an active research area in geometric learning. The unique setting of our problem, with large graphs that change structure with every event, makes parallelizing the inference step particularly challenging.
A future research project's ultimate goal would be to combine these four R&D threads into a generic pipeline for HEP pattern recognition that operates on heterogeneous data at different scales, from raw data to particles.
[1 ]Farrell, S., Calafiura, P., et al. . Novel deep learning methods for track reconstruction. (2018). arXiv. https://doi.org/10.48550/arXiv.1810.06111
 Ju, X., Murnane, D., et al. Performance of a geometric deep learning pipeline for HL-LHC particle tracking. Eur. Phys. J. C 81, 876 (2021). https://doi.org/10.1140/epjc/s10052-021-09675-8
 Hewes, J., Aurisano, A., et al. Graph Neural Network for Object Reconstruction in Liquid Argon Time Projection Chambers. EPJ Web of Conferences 251, 03054 (2021).
 Akram, A., & Ju, X. Track Reconstruction using Geometric Deep Learning in the Straw Tube Tracker (STT) at the PANDA Experiment. (2022) arXiv. https://doi.org/10.48550/arXiv.2208.12178
 Caillou, S., Calafiura, P. et al. ATLAS ITk Track Reconstruction with a GNN-based pipeline. (2022). ATL-ITK-PROC-2022-006. https://cds.cern.ch/record/2815578
 Lazar, A., Ju, X., et al. Accelerating the Inference of the Exa.TrkX Pipeline. (2022). arXiv. https://doi.org/10.48550/arXiv.2202.06929
 Wang, C., Ju, X., et al. Reconstruction of Large Radius Tracks with the Exa.TrkX pipeline. (2022). arXiv. https://doi.org/10.48550/arXiv.2203.08800
 Gumpula, K., et al., Graph Neural Network for Three Dimensional Object Reconstruction in Liquid Argon Time Projection Chambers. (2022). Presented at the Connecting the Dots 2022 workshop.
 Acharya, N., Liu, E., Lucas, A., Lazar, A. Optimizing the Exa.TrkX Inference Pipeline for Manycore CPUs. (2022). Presented at the Connecting the Dots 2022 workshop. https://indico.cern.ch/event/1103637/contributions/4821918
 Liu, R., Murnane, D., et al. Hierarchical Graph Neural Networks for Particle Reconstruction. (2022). Presented at the ACAT 2022 conference. https://indico.cern.ch/event/1106990/contributions/4996236/
 Murnane, D., Caillou, S.,. Heterogeneous GNN for tracking. (2022). Presented at the Princeton Mini-workshop on Graph Neural Networks for Tracking. https://indico.cern.ch/event/1128328/contributions/4900744
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