Graph Neural Networks for Charged Particle Tracking

Research at Princeton University with IRIS-HEP
Since July 2022

The reconstruction of charged particle trajectories ("tracking") in particle physics detectors is one of the computationally most challenging tasks of the field, limiting the amount of high-quality data that can even be recorded. Applied to particle collider experiments such as the CMS experiment, this task is different from many other problems that involve trajectories: There are millions of particle collisions per second, each with thousands of individual particles that need to be tracked, there is no time information (the particles travel too fast), and we do not observe a continuous trajectory but instead only 5-15 points ("hits") along the way in different detector layers. The task can be described as a combinatorically very challenging "connect-the-dots" problem, essentially turning a cloud of points (hits) in 3D space into a set of O(1000) trajectories.

Unlike traditional tracking algorithms built around Kalman filters, this project uses graph neural networks for significant speed increases. A conceptually simple way to turn tracking into a machine learning task is to create a fully connected graph of all points and then train an edge classifier to reject any edge that doesn't connect points that belong to the same particle. In this way, only the individual trajectories remain as components of the initial fully connected graph. In this project, we instead explore the idea of object condensation or learned clustering, where a network maps all hits to a latent space, learning to place hits from the same track close to each other, such that simple operations can recover the hits belonging to the same tracks.

Calibration factors for the Belle II Full Event Interpretation algorithm.
Charged particle tracking as an embedding task: The left side shows a tSNE embedding of all hit features, with hits belonging to some (randomly selected) particles colored. Our embedding maps hits belonging to the same particle in the same place (right picture), such that tracks can be recovered by a simple clustering operation.

Coordinating Software Training and Education efforts in High Energy Physics

Experimental high energy physics at large experiments is tasked with analyzing petabytes of data, necessitating an ever-evolving, ever more complex software stack. Delivering the best possible science depends crucially on the software skills of a large workforce of researchers. Keeping up with the latest big data tools and technology requires extensive training, covering everything from programming best practices to the latest industry tools and experiment-specific software frameworks.

From 2020 to 2022, I led the Belle II Software Training and Documentation group (Belle II Structure) that organizes training events and provides training material, primarily focusing on getting researchers up to speed with the Belle II software framework. In 2020 and since 2022, I have also been coordinating software training across experiments as one of the conveners of the HSF Training Group. I have also taught the basics of programming paradigms and software design patterns to more than 500 participants.

The HSF Training Center
Part of the new HSF Software Training Center that serves as an entry point for anyone wishing to learn with our materials.

Past projects

\(\bar B\longrightarrow D^*\ell^-\bar\nu_\ell\) Decays with Hadronic Tagging at Belle

PhD research at LMU Munich
2018 - June 2022

The decay \(\bar B\longrightarrow D^*\ell^-\bar\nu_\ell\) is used to precisely determine the CKM matrix element \(|V_{cb}|\), an important ingredient for tests of the flavor sector of the Standard Model. It is also the normalization channel for measurements of \(R(D^*)\), one of the key quantities of the flavor anomalies that recently sparked a flurry of interest in the field. Improving our understanding of \(\bar B\longrightarrow D^*\ell^-\bar\nu_\ell\) might help to understand and improve analyses of \(R(D^*)\) as well.

Reconstruction of a tag side \(B\) meson in addition to the semileptonically decaying \(B\) allows for a very clean data sample. Using the large Belle dataset but applying Belle II software for analysis, we can improve upon previous studies: The Belle II Full Event Interpretation, a machine learning algorithm to reconstruct the tag side \(B\) meson is almost two times more efficient than previously used algorithms. However, careful calibration studies are needed to address inconsistencies in its efficiency between data and Monte Carlo simulation.

Calibration factors for the Belle II Full Event Interpretation algorithm.
Calibration factors for the Belle II Full Event Interpretation algorithm.

Clustering of kinematic graphs

PhD research at LMU Munich
New Physics can manifest itself in kinematic distributions of particle decays. The parameter space defining the shape of such distributions can be large which is challenging for both theoretical and experimental studies. Using clustering algorithms, the parameter space can however be dissected into subsets (clusters) which correspond to similar kinematic distributions. Clusters can then be represented by benchmark points, which allow for less involved studies and a concise presentation of the results. To demonstrate this concept, I have written the Python package ClusterKinG, an easy to use framework for the clustering of distributions that particularly aims to make these techniques more accessible in a High Energy Physics context. As a physics use case its application has been demonstrated for the kinematic distributions of \(\bar B \longrightarrow D^{(*)}\tau^-\bar\nu_\tau\).
Example plot produced by ClusterKinG
Example plot produced by ClusterKinG: clustering of a a three dimensional parameter space results in three distinct clusters. Benchmark points are highlighted with enlarged markers.

Belle II Software Integration and Performance Testing

since 2018
Since 2018 I am the maintainer of the Belle II validation framework that tests the working and overall performance of the Belle II software. Each software package provides a selection of scripts (Python or C++) that run on small scale realistic data samples. The validation framework resolves dependencies between these scripts, executes them on a central server and uses different metrics to detect inconsistentencies and performance degradations. The results are visualized on a dynamic website.
Website showing the detailed results of the validation package.
Web server reporting on the detailed results of the latest validation run.

Construction of Angular Observables Sensitive to New Physics in \(\bar B\longrightarrow D^* \tau^-\bar\nu_\tau\) Decays and Measurements of Differential Cross Sections of \(\bar B\longrightarrow D^*\ell^-\bar\nu_\ell\) Decays with Hadronic Tagging at Belle

Thesis (M. Sc.) at LMU Munich, TU Munich

Recent measurements of \(\bar B\longrightarrow D^{(*)}\ell^-\bar\nu_\ell\) at Belle, BaBar and LHCb challenge lepton universality and thus the Standard Model at a combined confidence level close to four standard deviations. New measurements of differential decay rates could contribute to the understanding of these anomalies.

The differential cross section of the decay \(\bar B\longrightarrow D^*(\rightarrow D\pi)\ell^-\bar\nu_\ell\) is parametrized according to different dependencies on the three decay angles and the coupling constants of potential new physics contributions. Observables using binned measurements of the differential cross section are characterized and explicitly constructed. Based on an estimate for the obtainable sensitivity, optimal binnings for such measurements are discussed. The discriminatory power of the thus constructed observables is discussed based on a basis of dimension six operators with renormalizable couplings contributing to \(\bar B\longrightarrow D^*\ell^-\bar\nu_\ell\).

Furthermore, continuing work on an analysis of the \(\bar B\longrightarrow D^*(\rightarrow D\pi)\ell^-\bar\nu_\ell\) decay channel for \(\ell = e, \mu\) using data from the Belle detector at KEKB is presented. The events are selected from 772 million \(e^+e^- \longrightarrow \Upsilon(4S) \longrightarrow B\bar B\) events, where one \(B\) meson is fully reconstructed in hadronic modes. Unfolded differential decay rates in four kinematic variables are presented separately for \(\ell= e, \mu\) and a combined fit, allowing for precise calculations of \(|V_{cb}|\) and \(B\longrightarrow D^*\) form factors. The new lepton flavor specific results are also expected to impact the discussion about potential light lepton flavor universality violations prompted by measurements of \(B\longrightarrow K^{(*)}\ell\ell\) decays.

World averages for the measurements of R(D), R(Dstar)
The world average for the measurements of the observables \( R(D^{(*)}) \) currently shows a \( 4\sigma \) deviation from the Standard Model. Result of the Heavy Flavor Averaging Group from 2017.

Complex Organic Molecules in Protoplanetary Disks

Summer Project at TITECH
July 2017 till September 2017

Complex Organic Molecules (COMs) in protoplanetary disks have been the subject of extensive studies using chemical reaction networks (CRNs) (e.g. Walsh et al., 2014). The accuracy of these models depends on our knowledge of the relevant chemical processes. Some classes of reactions have been comprehensively studied, resulting in large databases like the UMIST database of astrochemistry, which lists more than 6000 gas-phase reactions. However, other classes of reactions, such as grain-surface reactions, still pose challenges.

By expanding the previously studied CRNs with additional grain-surface reactions that are currently studied in new laboratory experiments (and have so far mostly been considered in the context of meteorites), we tried to improve the description of COM formation in protoplanetary disks. More specifically, I have been using the existing simulation code to investigate the influence of physical and chemical parameters, such as temperature, density and activation energies, on the time evolution of the chemistry found on grains. Trying to automize some time-consuming manual tasks necessary for such studies, I wrote a framework to repeatedly run the simulation with different settings and to visualize the resulting datasets. This framework will enable future students to conduct similar studies much more efficiently, thereby opening new research possibilities.

Flowchart of the analysis framework I wrote
Analysis framework, repeatedly calling the chemical reaction network (CRN), storing output and log files, parsing them and finally bringing them together for plotting/analysis.

Performance monitoring for LHCb DAQ

July 2015 till September 2015

In 2020 the Data Acquisition (DAQ) of the LHCb experiment will be updated to feature a trigger-free readout. This requires an event builder network consisting of about 500 nodes with a total network capacity of 4 TBytes/s. DAQPIPE (Data Acquisition Protocol Independent Performance Evaluator) is a tool to simulate and evaluate the performance of such a DAQ system. The current implementation of DAQPIPE only gives rough feedback about the event building rate.

The aim of this 10-week summer student project was to implement network monitoring for a more detailed performance evaluation of different transport protocols and to spot potential bottlenecks. First, several existing performance monitors were tested. To that end DAQPIPE was run together with Tau and the obtained performance data was plotted with ParaProf, JumpShot and Vampir. In the second stage of the project, a light-weight performance analysis tool was written from scratch by wrapping around the C++ MPI communication library to collect data.

Monitoring data sent by two readout units
Monitoring the data sent by two readout units (RUs). RUs collect incoming data fragments from different subdetectors and send it to builder units (BUs), which process the information.

Truth-level based estimation of the sensitivity to pMSSM models in events with one hard lepton

Thesis (BA Sc. in Physics) at LMU Munich
Based on the search for supersymmetry in final states containing one isolated lepton, jets and missing transverse momentum with proton-proton collision data recorded with the ATLAS detector at a center-of-mass energy of \( \sqrt s \) = 8 TeV in 2012, I looked into the estimation of the sensitivity to phenomenological MSSM models using the signal shape of truth level signal samples. These were then compared to the sensitivity as calculated with MC samples on which a full detector simulation and reconstruction had been performed. The agreement was found to be generally low. Several sources of error were ruled out, showing the necessity of a more detailed study of the underlying truth- and reco-level signal samples.
CLs values obtianed by reco/truth level analysis
Comparing the CLs values obtained by reco level analysis (y axis) and truth level analysis (x axis). Ideally both values should roughly agree (resulting in the red line with \( x=y \)), but this is obviously not the case here.

Elliptic Functions

Thesis (BA Sc. in Mathematics) at LMU Munich

Central subject of the this are so called elliptic functions, meromorphic functions that are periodic in two directions, i.e. invariant under a translation of their argument by two linearly independent complex numbers.

Among others, elliptic functions are of great use in number theory, in particular there are interesting connections to sums of divisors of natural numbers. Furthermore they are used in the theory of elliptic curves and elliptic integrals.

Imaginary part of the Weierstrass p function
Imaginary part of the Weierstrass p function \( \wp \), an example of an elliptic function. Clearly visible are the two periods \( \wp(x+2) = \wp(x) = \wp(x+2i) \) throughout the domain.