Generative adversarial networks are known as a tool for fast simulation of data. Our aim is to research and develop a physical application of these tools by simulating LHCb hadron calorimeter (HCAL) in order to speed up the Monte Carlo datasets production

Lancierini, D.

Owen, P.

Serra, N.

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DOI 10.1393/ncc/i2019-19197-3Colloquia: IFAE 2018IL NUOVO CIMENTO 42 C (2019) 197Simulating the LHCb hadron calorimeter with generativeadversarial networksD. Lancierini, P. Owen and N. SerraPhysik-Institut, Universität Zürich - Zürich, Switzerlandreceived 31 January 2019Summary. — Generative adversarial networks are known as a tool for fast simula-tion of data. Our aim is to research and develop a physical application of these toolsby simulating LHCb hadron calorimeter (HCAL) in order to speed up the MonteCarlo datasets production.1. – Lepton flavour universality tests1.1. Current status for R(D(∗)). – Some of the most interesting phenomena reported byparticle physics experiments in the last few years are the numerous hints of lepton flavouruniversality (LFU) violation observed in semi-leptonic B decays. LFU can be tested withB meson semi-leptonic decays by measuring the ratio of the relative branching fractionsinvolving different lepton flavour types. An example of such a ratio is known as R(D(∗)):(1) R(D(∗)) =B(B → D(∗)τν)B(B → D(∗)μν)Recent measurements [1] have shown an enhancement of the ratio defined in eq. (1)compared to the Standard Model (SM) prediction [2]. Currently the world average ofthe combined measurements of R(D(∗)) deviates from the SM prediction by 3.62 σ [3].This might hint to a LFU-violating contribution of New Physics (NP) origin thatcouples mainly to the third generation of quarks and leptons, enhancing the b → τtransition.1.2. The R(D) measurement at LHCb. – The measurement of R(D) is currently ongo-ing at LHCb and the data collected by the experiment is more than enough to performthe analysis; a more pressing issue is the availability of Monte Carlo (MC) simulateddata to describe the effect of the detector on the signal and background processes.Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 D. LANCIERINI et al.2. – Fast simulation techniques2.1. The hadron calorimeter . – The LHCb hadron calorimeter (HCAL) [4] implements∼70% of Level 0 trigger in the presence of high-pt hadrons, and consists of a transverselysegmented plastic scintillator composed by cells of two different sizes. It is characterisedby moderate energy resolution although sufficient for trigger purposes. The simulationof the LHCb calorimeter response occupies a large fraction of the computing time forMC production. This work addresses the issue of simulating the LHCb calorimeter byparametrising its response using fast machine learning simulation techniques.2.2. Adversarial networks. – The neural network architectures which this work is basedon are known as Deep Convolutional Generative Adversarial Networks (DCGANs) andwere firstly introduced by Ian Goodfellow in ref. [5]. These architectures, which have beenthe subject of intense study (see, for example, ref. [6]), are a class of unsupervised neuralnetworks which consist of two neural networks: a generator (G) and a discriminator (D).In the training cycle, G learns a function that maps a uniformly distributed variable zto the dataset x and produces fake samples of data, while D learns to distinguish thefake samples G(z) from the real dataset. These two networks play a non-cooperativeminimax game with the following value function V (G,D) [5]:(2) minGmaxDV (D,G) = Ex∼pdata(x)logD(x) + Ez∼pz(z)log(1 − D(G(z))).The training cycle ends when D has a discrimination rate of 50%, and G is trained toreproduce fake samples distributed as close as possible to the real dataset. The existenceof such equilibrium is not guaranteed but several attempts have been made to helpoptimise its search, as shown in ref. [6].2.3. Generative models for the LHCb HCAL. – In order to parametrise the LHCbHCAL using neural networks we tested different architectures on the same dataset. Thisdataset was generated using PGun and consists of several events in which a single pionhits the calorimeter at different positions and with variable pt. In order to fully exploit theadvantages of a convolutional network, each event in the dataset is converted to an image.The values of non-zero pixels and their locations are determined by the reconstructedenergy and location of each calorimeter cell. The architectures tested in this work areConditional DGCANs [7] and BicycleGANs [8], since they both provide a control on theinput as well as a stochastic output.Fig. 1. – Pions Et distribution in the MC truth (left), as reconstructed by the MC (center) andas simulated by the cDCGAN (right).SIMULATING THE LHCb HADRON CALORIMETER ETC. 3Fig. 2. – Absolute trigger efficiency (left) and relative trigger efficiency (right) comparison be-tween MC and cDCGAN.Fig. 3. – Pions Et distribution in the MC truth (left), as reconstructed by the MC (center) andas simulated by the BicycleGAN (right).3. – Architectures’ comparison3.1. Conditional DCGAN (cDCGAN). – We trained a cDCGAN network on a sampleof ∼3.6 × 104 single-pion events with energies spanning 0  Et  25GeV. In the caseof the cDCGAN, the network input consists of a string of (x, y,Et). Once the networktraining was completed, the network was tested on a test set which is disjoint from thetraining set. The results are plotted in fig. 1. In each of the panels the distribution ofthe sum over all energies recorded in each cell per event is plotted. The panel on theleft shows the distribution of the true Et as simulated by the tracking, while the centralpanel displays the distribution of the HCAL reconstructed Et as simulated by the MC.The plot on the right shows the reconstructed Et as simulated by the cDCGAN.Fig. 4. – Absolute trigger efficiency (left) and relative trigger efficiency (right) comparison be-tween MC and BicycleGAN.4 D. LANCIERINI et al.More importantly our aim is to emulate the HCAL trigger efficiency, i.e., the ratiobetween number of events that fire the trigger and the total number of events. The resultsfor such comparison is shown in fig. 2. The network took and average of 2.98× 10−3 s togenerate one event on an NVidia Tesla P100 GPU.3.2. BicycleGAN . – We trained a BicycleGAN [8] on the same dataset. This architec-ture is more complex than the cDCGAN, as it takes as input images rather than strings.The comparison between the distributions of total energy per event is shown in fig. 3.As shown in fig. 4 the emulation of the trigger efficiency is more accurate in the caseof BycycleGAN, although the augmented complexity of the network slows the speed ofproduction to an average of 4.79 × 10−3 s per event on the same hardware.4. – ConclusionsAs shown in this work, generative adversarial networks provide a useful tool for fastMC production, although further research is needed in order to assess the scalability oftheir application to the simulation of LHCb HCAL response to a full event.REFERENCES[1] LHCb Collaboration, Phys. Rev. Lett., 120 (2018) 171802.[2] Bigi D., Gambino P. and Schacht S., Phys. Rev. D, 94 (2016) 094008.[3] Amhis Y. et al., Averages of b-hadron, c-hadron, and τ -lepton properties as ofsummer 2014, arXiv:1412.7515; updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/.[4] Pereima D., J. Instrum., 12 (2017) C06016.[5] Goodfellow I. J. et al., Generative Adversarial Networks, arXiv:1406.2661 (2014).[6] Salimans T. et al., Improved Techniques for Training GANs, arXiv:1606.03498 (2016).[7] Mirza M. et al., Conditional Generative Adversarial Nets, arXiv:1411.1784v1 (2014).[8] Zhu J. et al., Toward Multimodal Image-to-Image Translations, arXiv:1711.11586 (2014).

Simulating the LHCb hadron calorimeter with generative

adversarial networks

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Simulating the LHCb hadron calorimeter with generative adversarial networks

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