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DijetGAN: A Generative-Adversarial Network Approach for the Simulation of QCD Dijet Events at the LHC
Riccardo Di Sipio, Michele Faucci Giannelli, Sana Ketabchi Haghighat, Serena Palazzo
TL;DR
LHC experiments face the computational burden of generating large simulated event samples and simulating detector response. This paper trains a convolutional GAN on simulated dijet events and reports good agreement with Monte Carlo kinematic distributions at particle and reco levels.
Problem
Generating the large simulated samples needed by LHC experiments is computationally demanding, including for detector simulation.
Source: §1 · pp. 2, 4Method
Results
The GAN reproduces simulated events with high accuracy, with satisfactory agreement across particle- and reco-level kinematic distributions.
Source: §6 · p. 8, §8 · p. 13Takeaways & Limitations
The GAN offers a way to reduce CPU use for event generation and may support use of computationally demanding generators in LHC analyses.
Source: §8 · p. 13
Abstract
from arXiv · showhide
A Generative-Adversarial Network (GAN) based on convolutional neural networks is used to simulate the production of pairs of jets at the LHC. The GAN is trained on events generated using MadGraph5 + Pythia8, and Delphes3 fast detector simulation. We demonstrate that a number of kinematic distributions both at Monte Carlo truth level and after the detector simulation can be reproduced by the generator network with a very good level of agreement. The code can be checked out or forked from the publicly accessible online repository https://gitlab.cern.ch/disipio/DiJetGAN .
1 Introduction
The paper presents a convolutional GAN for simulating LHC dijet events, motivated by the computational burden of conventional event generation and detector simulation. It reports improved reproduction of kinematic distributions through convolutional layers and attention to process symmetries.
1 Introduction
- Earlier GAN studies reported weaker kinematic agreement or a failure to learn left-right symmetry, while other work incorporated process symmetries.The paper situates its approach alongside VAE methods and prior GAN applications to calorimeter response.Source: §1 · p. 2
- The convolutional GAN reproduces kinematic distributions better than previous attempts, with the improvement attributed to accounting for more process symmetries.The paper also identifies deep convolutional layers as part of the approach.Source: §1 · p. 3
- A GAN maps random noise to physical samples while a discriminator distinguishes generated samples from training data; training seeks a generator distribution close to the data distribution.Source: §1 · p. 3
- Dijet production is a ubiquitous background to Standard Model precision measurements and searches for physics beyond the Standard Model.Source: §1 · p. 3
- Conventional event generation and detector simulation are computationally demanding, motivating fast simulation approaches for LHC experiments.The passage notes that advanced generators are too time-consuming for billions of events and that detector simulation also takes substantial time.Source: §1 · pp. 2, 4
2 Physics of QCD dijet events
QCD dijet events arise when colliding partons produce two jets, and their kinematic distributions are important both for simulation and for searches at high invariant mass. The section identifies the distributions used to assess agreement between Monte Carlo and GAN output.
2 Physics of QCD dijet events
- QCD dijet events are formed when two outgoing partons produce a pair of jets, which are reconstructed from particle clusters using a clustering algorithm.Source: §2 · p. 4
- Dijet invariant mass and production angle distributions are important because new massive particles could distort them, especially above 1 TeV.The QCD invariant-mass distribution is described as smooth and monotonically decreasing.Source: §2 · p. 5
- Agreement is evaluated using the transverse momentum, pseudorapidity, and mass distributions of individual jets and the dijet system, with χ2 as the figure of merit.Source: §2 · p. 5
3 Monte Carlo Sample
The training sample consists of MadGraph5 and Pythia8 dijet events, with detector response simulated by Delphes3 using ATLAS-like settings. Selection and reconstruction define the particle- and reco-level samples used in training.
3 Monte Carlo Sample
- The sample contains 10 million MadGraph5 and Pythia8 dijet events, with Delphes3 fast simulation and an average of 25 overlaid pile-up collisions.The sample corresponds to about 0.5 fb−1 of integrated luminosity.Source: §3 · p. 5
- Particle-level and reco-level refer to reconstruction before and after detector simulation, respectively; jets use anti-kT with R = 1.0.Particle-level includes stable final-state particles and unstable particles intended for later detector simulation.Source: §3 · p. 5
- The HT > 500 GeV selection yields about 7.5 million particle-level events and 4 million reco-level events for training.The selection increases events with both jets having pT > 250 GeV.Source: §3 · p. 5
- Pseudorapidity η describes a particle's angle relative to the beam axis and relates to momentum through |p| = pT cosh η.Source: §3 · p. 5
4 Network Architecture
The network uses convolutional generator and discriminator blocks, with the generator mapping uniform random inputs to seven jet-kinematic features. Training uses distinct generator and discriminator losses and Adam optimization.
4 Network Architecture
- The generator and discriminator are convolutional networks connected by feeding the generator output into the discriminator input.Source: §4 · p. 6, Figure 1 · p. 6
- The generator maps 128 uniform random values in [0, 1] to seven features describing the two leading jets.The features are the leading jet's pT, η, and mass, and the second-leading jet's pT, η, φ, and mass.Source: §4 · p. 6
- The generator uses mean squared error and the discriminator binary cross-entropy, with Adam at learning rate 10−5, β1 = 0.5, and β2 = 0.9.All layers use LeakyReLU except the generator and discriminator output layers, which use tanh and sigmoid, respectively.Source: §4 · p. 6
5 Training
Training exploits dijet symmetries through azimuthal and pseudorapidity transformations. The generator and discriminator reach a stationary state after a few thousand epochs, while agreement continues improving until about 100,000 epochs at both reconstruction levels.
5 Training
- Azimuthal symmetry fixes the leading jet's φ to zero and represents the other jet's φ as the absolute difference between the two jets' angles.The azimuthal transformation is reversed when events are generated.Source: §5 · pp. 6–7
- Each event is also used with both pseudorapidity signs reversed, and random η flips during generation remove nonphysical effects.Source: §5 · p. 7
- After a few thousand epochs the generator and discriminator reach a stationary state, while χ2 agreement continues improving until about 100,000 epochs at both levels.Figures 2 and 3 plot discriminator and generator losses against training epoch at particle and reco level, respectively.Source: §5 · p. 7, Figure 2 · p. 7, Figure 3 · p. 8
6 Event Generation and Final Results
The GAN reproduces kinematic distributions over a broad range and shows agreement with a four-parameter fit in the high-mass region. Unlike that fit, it generates events rather than only estimating a background for one observable.
6 Event Generation and Final Results
- The GAN shows satisfactory agreement with Monte Carlo across a large kinematic range at both particle and reco levels.Figures 4 and 5 compare the two leading jets and dijet system with particle- and reco-level Monte Carlo, respectively.Source: §6 · p. 8, Figure 4 · p. 9, Figure 5 · p. 10
- Training on about 150,000 events with mjj >1.5 TeV yielded a GAN sample of about 1 million events for the high-mass study.The high-mass region is of particular interest for searches beyond the Standard Model.Source: §6 · p. 11
- χ2/NDF = 1.3 for the 4p analytic fit over 2.5–10 TeV, while the GAN shows similar agreement in that region.Figure 7 compares the Monte Carlo sample, GAN extrapolation, and fitted function.Source: §6 · p. 11, Figure 7 · p. 11
- Unlike the 4p fit, which estimates multijet background for one observable, the GAN generates events that can broaden background-determination techniques.The 4p function is motivated by parton distribution functions and has been widely used by Tevatron and LHC experiments.Source: §6 · p. 11
7 Possible extensions of the method
The extensions address more flexible event representations and targeted sampling. The paper reports that both extensions were implemented and produced results compatible with those presented earlier.
7 Possible extensions of the method
- Both proposed method extensions were implemented and produced results compatible with those presented earlier; the code is available in the repository.Source: §7 · p. 12
7.1 Arbitrary number of input variables
- For arbitrary input-variable counts, PCA or an autoencoder can map events into a lower-dimensional latent representation for GAN training, then decode generated events back to physical variables.The autoencoder chain maps R^N to R^M and back to R^N, with M < N.Source: §7.1 · p. 12
7.2 Conditioning on external variable
- Variable conditioning adds a parameter controlling noise-to-event transformation, allowing sampling to be biased toward chosen kinematic ranges without event weights.Examples include dijet mass, dijet transverse momentum, pile-up, and pairs of pMSSM masses.Source: §7.2 · pp. 12–13
8 Conclusions and Outlook
The authors present the GAN as a proof of concept for reproducing simulated events with high accuracy and potentially reducing event-generation resource use. They identify broader processes and training stability as directions for future work.
8 Conclusions and Outlook
- The GAN reproduces simulated events with high accuracy, demonstrating potential for efficiently producing the large event samples required by LHC experiments.Source: §8 · p. 13
- The approach may be generalized to top-quark pairs and vector-boson production with jets, processes whose best Monte Carlo predictions also have high CPU requirements.Source: §8 · p. 13
- Future work will target more stable training, avoidance of model collapse, and fitting relevant kinematic distributions in low-cross-section regions.Source: §8 · p. 13
Appendix
The appendix tests the GAN on all-hadronic top-quark-pair events, whose jet-mass distribution can be bimodal. The GAN output agrees satisfactorily with particle-level Monte Carlo in the comparison shown.
Appendix
- The GAN output agrees satisfactorily with particle-level MadGraph5+Pythia8 Monte Carlo for the all-hadronic top-pair kinematic observables.Figure 8 compares the MC prediction (gray) with the GAN output (black).Source: Appendix · p. 14, Figure 8 · p. 14
- The sample selection uses H_T > 700 GeV, jet p_T > 350 GeV, and jet mass < 500 GeV; selected jets can have top-mass or W-mass peaks.The corresponding simulated masses are 172.5 GeV for the top quark and 80.4 GeV for the W boson.Source: Appendix · p. 14
- The jet-mass distribution is bimodal because some events contain only the W boson within ΔR < 1.0 of the jet axis, and the GAN receives neither particle mass as input.The network must infer the top-quark and W-boson masses during training.Source: Appendix · p. 14