For the past year, the HEP.TrkX project has been investigating machine learning solutions to LHC particle track reconstruction problems. A variety of models were studied that drew inspiration from computer vision applications and operated on an image-like representation of tracking detector data. While these approaches have shown some promise, image-based methods face challenges in scaling up to realistic HL-LHC data due to high dimensionality and sparsity. In contrast, models that can operate on the spacepoint representation of track measurements ("hits") can exploit the structure of the data to solve tasks efficiently. In this paper we will show two sets of new deep learning models for reconstructing tracks using space-point data arranged as sequences or connected graphs. In the first set of models, Recurrent Neural Networks (RNNs) are used to extrapolate, build, and evaluate track candidates akin to Kalman Filter algorithms. Such models can express their own uncertainty when trained with an appropriate likelihood loss function. The second set of models use Graph Neural Networks (GNNs) for the tasks of hit classification and segment classification. These models read a graph of connected hits and compute features on the nodes and edges. They adaptively learn which hit connections are important and which are spurious. The models are scaleable with simple architecture and relatively few parameters. Results for all models will be presented on ACTS generic detector simulated data.

Particle track reconstruction in dense environments such as the detectors of the High Luminosity Large Hadron Collider (HL-LHC) is a challenging pattern recognition problem. Traditional tracking algorithms such as the combinatorial Kalman Filter have been used with great success in LHC experiments for years. However, these state-of-the-art techniques are inherently sequential and scale poorly with the expected increases in detector occupancy in the HL-LHC conditions. The HEP.TrkX project is a pilot project with the aim to identify and develop cross-experiment solutions based on machine learning algorithms for track reconstruction. Machine learning algorithms bring a lot of potential to this problem thanks to their capability to model complex non-linear data dependencies, to learn effective representations of high-dimensional data through training, and to parallelize easily on high-throughput architectures such as GPUs. This contribution will describe our initial explorations into this relatively unexplored idea space. We will discuss the use of recurrent (LSTM) and convolutional neural networks to find and fit tracks in toy detector data.

To address the unprecedented scale of HL-LHC data, the Exa.TrkX project is investigating a variety of machine learning approaches to particle track reconstruction. The most promising of these solutions, graph neural networks (GNN), process the event as a graph that connects track measurements (detector hits corresponding to nodes) with candidate line segments between the hits (corresponding to edges). Detector information can be associated with nodes and edges, enabling a GNN to propagate the embedded parameters around the graph and predict node-, edge- and graph-level observables. Previously, message-passing GNNs have shown success in predicting doublet likelihood, and we here report updates on the state-of-the-art architectures for this task. In addition, the Exa.TrkX project has investigated innovations in both graph construction, and embedded representations, in an effort to achieve fully learned end-to-end track finding. Hence, we present a suite of extensions to the original model, with encouraging results for hitgraph classification. In addition, we explore increased performance by constructing graphs from learned representations which contain non-linear metric structure, allowing for efficient clustering and neighborhood queries of data points. We demonstrate how this framework fits in with both traditional clustering pipelines, and GNN approaches. The embedded graphs feed into high-accuracy doublet and triplet classifiers, or can be used as an end-to-end track classifier by clustering in an embedded space. A set of post-processing methods improve performance with knowledge of the detector physics. Finally, we present numerical results on the TrackML particle tracking challenge dataset, where our framework shows favorable results in both seeding and track finding.

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.

Particle physics has an ambitious and broad experimental programme for the coming decades. This programme requires large investments in detector hardware, either to build new facilities and experiments, or to upgrade existing ones. Similarly, it requires commensurate investment in the R&D of software to acquire, manage, process, and analyse the shear amounts of data to be recorded. In planning for the HL-LHC in particular, it is critical that all of the collaborating stakeholders agree on the software goals and priorities, and that the efforts complement each other. In this spirit, this white paper describes the R&D activities required to prepare for this software upgrade.