Source-linked AI summary
How to GAN LHC Events
Anja Butter, Tilman Plehn, Ramon Winterhalder
TL;DR
LHC event simulation faces challenges from high-dimensional phase-space coverage, inefficient event unweighting, and computationally expensive detector simulation. The paper uses an MMD-enhanced GAN to generate top-pair events while describing on-shell resonances and other sharp phase-space structures. The resulting network reproduces full phase-space behavior, including distributions, resonance structures, and tails, within the demonstrated setting.
Problem
LHC simulations must efficiently cover high-dimensional phase space and represent sharp resonance structures, while event unweighting and detector simulation remain costly challenges.
Method
The paper trains a GAN with alternating generator-discriminator losses and adds maximum mean discrepancy to compare true and generated distributions and resolve localized phase-space features.
Results
The GAN reproduces full top-pair phase-space behavior, including flat distributions, intermediate on-shell resonances, tails, and phase-space boundaries.
Takeaways & Limitations
MMD-enhanced GAN event generation can represent realistic LHC phase-space structures from unweighted training events and generate arbitrarily many new events with the same phase-space information.
Takeaways & Limitations
GAN training can suffer stability issues from the generator-discriminator balance, and learning limitations can arise from finite training statistics.
Abstract
from arXiv · showhide
Event generation for the LHC can be supplemented by generative adversarial networks, which generate physical events and avoid highly inefficient event unweighting. For top pair production we show how such a network describes intermediate on-shell particles, phase space boundaries, and tails of distributions. In particular, we introduce the maximum mean discrepancy to resolve sharp local features. It can be extended in a straightforward manner to include for instance off-shell contributions, higher orders, or approximate detector effects.
1 Introduction
The paper develops GAN-based LHC event simulation to address Monte Carlo challenges in high-dimensional phase space, event unweighting, and slow detector simulation. It demonstrates coverage of realistic multi-particle phase space, including on-shell resonances, tails, and boundaries, using an MMD-enhanced network.
- GANs are proposed as an additional tool for alleviating Monte Carlo challenges in phase-space coverage, event unweighting, and computationally expensive detector simulation.
- A remaining open problem is describing realistic multi-particle matrix elements across high-dimensional phase space in a flexible and generalizable way.
- The paper efficiently GANs 2 →6 particle production while describing intermediate on-shell states with Breit-Wigner propagators.
- Fast neural-network event generation could be combined with parton showers, hadronization, detector effects, and higher-order corrections when those effects are included in training data.
- The combined GAN-MMD network is applied to top-pair production with subsequent decays and targets full phase-space behavior, including intermediate on-shell particles.
2 Phase space generation
The paper frames phase-space generation as a problem of efficiently covering high-dimensional event distributions with sharp resonances, boundaries, and tails. It develops a GAN-based approach whose adversarial training is supplemented by MMD to resolve localized structures.
- Benchmark: Top-pair production with intermediate W-bosons provides the benchmark for studying phase-space generation.
- Phase-space structure: The six-particle final state leaves a 14-dimensional phase space after energy-momentum conservation, alongside a 2-dimensional integration over parton momentum fractions.
- Standard Monte Carlos: Standard sampling must identify important regions while precisely mapping narrow Breit-Wigner resonances and other dramatic amplitude features.
- Standard Monte Carlos: Event simulation additionally requires converting weighted phase-space points into uniformly weighted events, motivating methods that avoid inefficient unweighting.
- Generative adversarial network: The GAN trains a generator to mimic the true distribution and a discriminator to distinguish true from generated batches through alternating loss optimization.
- Generative adversarial network: Stable training requires balancing generator and discriminator performance, while gradient regularization addresses instability from their adversarial interplay.
- Loss functions for intermediate particles: The maximum mean discrepancy compares true and generated samples with a kernel-based distance whose kernel shape controls the locality of the comparison.
3 Machine-learning top pairs
The GAN is trained with an additional MMD loss to reproduce top-pair phase-space structures, including resonance peaks, tails, boundaries, and correlations. It matches broad distributions and angular coverage, generates events beyond the training sample, and satisfies momentum conservation at the order of 2%, while low training statistics limit tail accuracy.
- Setup: The benchmark generates 1 million 2 →6 events with on-shell intermediate tops and W bosons, using approximate Breit-Wigner propagators while omitting proper off-shell contributions.The setup can be extended to a proper off-shell description, but the balance between narrow on-shell and broad off-shell contributions would change.
- Flat distributions: The GAN reproduces energy, transverse-momentum, and angular distributions, with deviations reaching about 20% only in high-pT regions affected by low training statistics.For b-quarks, deviations begin near 150 GeV with roughly 25 tail events per batch; for top quarks, 10% deviations occur around pT,t ≳250 GeV where relative statistical uncertainty reaches 15%.
- Phase space coverage: The GAN matches flat azimuthal jet distributions and generates statistically independent events beyond the training sample, covering the full phase space up to 50 million generated events.The comparison uses 1 million true events and GAN samples of 1 million, 10 million, and 50 million events.
- Resonance poles: The additional MMD loss makes the GAN reproduce narrow W and top invariant-mass structures that it barely learns without MMD.Default kernel widths matched to Standard Model decay widths nearly reproduce the W mass distribution; the top peak remains somewhat less accurate because it depends on three-particle correlations.
- Correlations: The generated events reproduce the low-pT peak, intermediate plateau, and high-pT momentum-conservation boundary in b-quark–top correlations, except for statistically fluctuating boundary regions.The remaining asymmetry occurs where the normalized differential cross section has fallen below the visible range.
4 Outlook
The GAN reproduces the full phase-space structure of top-pair production while avoiding event unweighting, and can generate arbitrarily many events from the learned distribution. Its accuracy is limited by training statistics in poorly populated regions, while extensions to broader LHC simulation workflows remain possible.
- The GAN reproduces top-pair production across the full phase space down to the kinematics of six top-decay jets.
- An additional MMD kernel captures on-shell resonances and distribution tails using final-state momenta related to the resonances and their rough phase-space resolution.
- Relatively flat distributions can be reproduced at arbitrary precision, limited by the training-sample statistics, while resonance masses are extracted readily.
- The principal limitation is that statistical uncertainties in sparsely populated training-data tails become systematic uncertainties in the corresponding high-statistics generated samples.
- Because the GAN avoids event unweighting, it provides a fast addition to the LHC event-generation toolbox and can incorporate weighted coverage improvements or mixed data and Monte Carlo training.